# How many times has the Milky Way rotated?

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I would think that is a highly naive question, but I still ask it.

Given current experimentally discovered numbers:

• the Milky Way galaxy is ~13-14 billion years old
• At the galactic radius where our sun is, the rotational period is about 240 million years.

So, with nothing changing at all (the galaxy and stars pop fully formed into existence, the rotation period doesn't change), the galaxy has rotated roughly

~14/(1/4) = 50 to 60 times.

Since the assumptions are naive, what is a better approximation for the number of times? How long has the mass that is recognizable now as the Milky Way been rotating (and what has been the speed by radius over time)? Is it a lot more than 50 times and if so, has it been slowing down as a whole or just at the Sun's position, or a less because the coalescence into stars rotating took a few billion years to translate into the faster rotation which it is now mostly set at? Or some other reason which is more articulate?

Note: This question is similar to but distinct from The equation for how many times the Earth has revolved around the galaxy, as the title asks similarly what I'm asking but the content just asks for how to calculate rotational speed.

In general, Milky Way stars that are 13-14 billion old are part of the Galactic halo, and roughly spherical distribution of stars that contains the globular clusters. This part of the Galaxy formed first, and the flattened Galactic disk is more like 10 billion years old.

At that point, the disk had formed, and large-scale movements of mass were probably less likely than they were at earlier epochs, so it's likely a reasonable assumption to say that the mass interior to our current position in the Galaxy (which is what sets the orbital speed) hasn't changed a lot since then.

So probably using the same speed, but an age more like 10 billion years, would be more realistic - that yields 10/0.24 = 42.

So the answer to this question, as to some others, is 42. :-)

The question doesn't have a single answer, because the Milky Way's rotation is differential rather than solid-body. This means that stars in the inner part complete their rotation about the center in a shorter period of time than stars at a larger radius. Stars orbiting with a radius of 1 kpc (about 3,000 light years) will take about 30 million years to go once around; stars like the Sun, with orbital radii of about 8 kpc, will take about 220 million years; stars orbiting with a radius of 20 kpc will take about 500 million years.

If you mean "how many times has the narrow region of the Milky Way currently containing the Sun's orbit rotated" -- ELNJ's answer is probably reasonable, given that the last major merger contributing to the Milky Way's growth was probably about 10 billion years ago, so changes in the amount of mass inside the Solar radius (which would change the orbital timescales) were probably fairly small after that.

## The Rotation of the Milky

Differential Rotation. Oort's Formulas. The flatness of the Milky Way is already suggestive of a general rotation about an axis normal to the galactic plane. Observations of the motions both of stars and of interstellar gas have confirmed this rotation and shown it to be differential. This means that the angular velocity of rotation depends on the distance from the galactic centre (Fig. 17.13). Thus the Milky Way does not rotate like a rigid body. Near the Sun, the rotational velocity decreases with radius.

The observable effects of the galactic rotation were derived by the Dutch astronomer Jan H. Oort. Let us suppose the stars are moving in circular orbits about

a) Velocity w.r.t the Milky Way a) Velocity w.r.t the Milky Way

b) Velocity w.r.t the Sun

Fig. 17.13a-d. The effect of differential rotation on the radial velocities and proper motions of stars. (a) Near the Sun the orbital velocities of stars decrease outwards in the Galaxy. (b) The relative velocity with respect to the Sun is obtained by c) Radial velocity

subtracting the solar velocity from the velocity vectors in (a). (c) The radial components of the velocities with respect to the Sun. This component vanishes for stars on the same orbit as the Sun. (d) The tangential components of the velocities

Fig. 17.13a-d. The effect of differential rotation on the radial velocities and proper motions of stars. (a) Near the Sun the orbital velocities of stars decrease outwards in the Galaxy. (b) The relative velocity with respect to the Sun is obtained by subtracting the solar velocity from the velocity vectors in (a). (c) The radial components of the velocities with respect to the Sun. This component vanishes for stars on the same orbit as the Sun. (d) The tangential components of the velocities the galactic centre (Fig. 17.14). This approximation is acceptable for population I stars and gas. The star S, seen from the Sun © at galactic longitude l at distance r, has circular velocity V at a distance R from the centre. Similarly for the Sun the galactic radius and velocity are R0 and V0. The relative radial velocity vr of the star with respect to the Sun is the difference between the projections of the circular velocities on the line of sight:

Denoting the angular velocity of the star by w = V/R and that of the Sun by w0 = V0/R0, one obtains the observable radial velocity in the form vr = R0(w — w0) sinl.

where a is the angle between the velocity vector of the star and the line of sight. From Fig. 17.14 the angle CS© = a + 90°. By applying the sine theorem to the triangle CS© one obtains sin (a + 90°) _ R0 sin l R

The tangential component of the relative velocity of the Sun and the star is obtained as follows. From Fig. 17.14, vt = V sin a — V0 cos l = Rw sin a — R0w0 cos l. The triangle ©CP gives

R sin a = R0 cos l — r , and hence vt = R0(w — w0) cos l — wr . (17.9)

Oort noted that in the close neighbourhood of the Sun (r ^ R0), the difference of the angular velocities will be very small. Therefore a good approximation for the exact equations (17.8) and (17.9) is obtained by keeping only the first term of the Taylor series of w — w0 in the neighbourhood of R = R0:

Fig. 17.14. In order to derive Oort's formulas, the velocity vectors of the Sun and the star S are divided into components along the line ©S and normal to it

Using m = V/R and V(R0) = V0, one finds

For the tangential relative velocity, one similarly obtains, since rnr

Because 2 cos21 = 1 + cos 2l, this may be written vt

where A is the same as before and B, the second Oort constant, is

The proper motion ¡x = vt/r is then given by the expression

Equation (17.10) says that the observed radial velocities of stars at the same distance should be a double sine curve as a function of galactic longitude. This has been confirmed by observations (Fig. 17.15a). If the distance to the stars involved is known, the amplitude of the curve determines the value of the Oort constant A.

Independently of distance, the proper motions of the stars form a double sine wave as a function of galactic

Fig. 17.14. In order to derive Oort's formulas, the velocity vectors of the Sun and the star S are divided into components along the line ©S and normal to it vr [km/s]

Ro ^ r, the difference R — R0 r cos l. One thus obtains an approximate form vr [km/s]

where A is a characteristic parameter of the solar neighbourhood of the Galaxy, the first Oort constant:

Fig. 17.15a,b. The velocity components due to differential rotation according to Oort's formulas as functions of galactic longitude. (a) Radial velocities for objects at a distance of 1 and 2kpc. (Compare with Fig. 17.13.) Strictly, the longitude at which the radial velocity vanishes depends on the distance. Oort's formulas are valid only in the close vicinity of the Sun. (b) Proper motions

Fig. 17.15a,b. The velocity components due to differential rotation according to Oort's formulas as functions of galactic longitude. (a) Radial velocities for objects at a distance of 1 and 2kpc. (Compare with Fig. 17.13.) Strictly, the longitude at which the radial velocity vanishes depends on the distance. Oort's formulas are valid only in the close vicinity of the Sun. (b) Proper motions v

longitude, as seen in Fig. 17.15b. The amplitude of the curve is A and its mean value, B.

In 1927 on the basis of this kind of analysis, Oort established that the observed motions of the stars indicated a differential rotation of the Milky Way. Taking into account an extensive set of observational data, the International Astronomical Union IAU has confirmed the present recommended values for the Oort constants:

A = 15kms 1kpc 1, B = -10kms 1kpc

The Oort constants obey some interesting relations. By subtracting (17.13) from (17.11), one obtains

Knowing the values of A and B, one can calculate the angular velocity &>o = 0.0053"/year, which is the angular velocity of the local standard of rest around the galactic centre.

The circular velocity of the Sun and the LSR can be measured in an independent way by using extragalactic objects as a reference. In this way a value of about 220 km s-1 has been obtained for V0. Using (17.15) one can now calculate the distance of the galactic centre R0. The result is about 8.5 kpc, in good agreement with the distance to the centre of the globular cluster system. The direction to the galactic centre obtained from the distribution of radial velocities and proper motions by means of (17.10) and (17.14) also agrees with other measurements.

The orbital period of the Sun in the Galaxy according to these results is about 2.5 x 108 years. Since the Sun's age is nearly 5 x 109 years, it has made about 20 revolutions around the galactic centre. At the end of the previous revolution, the Carboniferous period had ended on Earth and the first mammals would soon appear.

The Distribution of Interstellar Matter. Radio radiation from interstellar gas, in particular that of neutral hydrogen, is not strongly absorbed or scattered by interstellar dust. It can therefore be used to map the structure

Fig. 17.16. Clouds P1, P2, various distances seen in the same direction at of the Milky Way on large scales. Radio signals can be detected even from the opposite edge of the Milky Way.

The position of a radio source, for example an HI cloud, in the Galaxy cannot be directly determined. However, an indirect method exists, based on the differential rotation of the Galaxy.

Figure 17.16 is a schematic view of a situation in which gas clouds on the circles P1, P2. are observed in the direction l (-90° < l < 90°). The angular velocity increases inwards, and therefore the greatest angular velocity along the line of sight is obtained at the point Pk, where the line of sight is tangent to a circle. This means that the radial velocity of the clouds in a fixed direction grows with distance up to the maximum velocity at cloud Pk :

where Rk = R0 sin l. The distance of cloud Pk from the Sun is r = R0 cos l. When r increases further, vr decreases monotonically. Figure 17.17 shows how the observed radial velocity in a given direction varies with distance r, if the gas moves in circular orbits and the angular velocity decreases outwards.

Fig. 17.17. The radial velocity as a function of distance (shown schematically)

The neutral hydrogen 21 cm line has been particularly important for mapping the Milky Way. Figure 17.18 gives a schematic view of how the hydrogen spectral line is made up of the radiation of many individual concentrations of neutral hydrogen, clouds or spiral arms. The line component produced by each cloud has a wavelength which depends on the radial velocity of the cloud and a strength depending on its mass and density. The total emission is the sum of these contributions.

By making observations at various galactic longitudes and assuming that the clouds form at least partly continuous spiral arms, the distribution of neutral hydrogen in the galactic plane can be mapped. Figure 15.17 shows a map of the Milky Way obtained from 21 cm line observations of neutral hydrogen. It appears that the neutral hydrogen is concentrated in spiral arms. However, interpretation of the details is difficult because of the uncertainties of the map. In order to obtain the distances to the gas clouds, one has to know the rotation curve, the circular velocity as a function of the galactic radius. This is determined from the same radial velocity observations and involves assumptions concerning the density and rotation of the gas. The interpretation of

Fig. 17.18. Clouds at different distances have different velocities and therefore give rise to emission lines with different Doppler shifts. The observed flux density profile (continuous curve) is the sum of the line profiles of all the individual line profiles (dashed curves). The numbers of the line profiles correspond to the clouds in the upper picture

Fig. 17.18. Clouds at different distances have different velocities and therefore give rise to emission lines with different Doppler shifts. The observed flux density profile (continuous curve) is the sum of the line profiles of all the individual line profiles (dashed curves). The numbers of the line profiles correspond to the clouds in the upper picture the spiral structure obtained from radio observations is also still uncertain. For example, it is difficult to fit the radio spiral structure to the one obtained near the Sun from optical observations of young stars and associations.

The Rotation, Mass Distribution and Total Mass of the Milky Way. In (17.17) the galactic longitude l gives the galactic radius Rk of the clouds with maximum radial velocity. By making observations at different longitudes, one can therefore use (17.17) to determine the angular velocity of the gas for various distances from the galactic centre. (Circular motions must be assumed.) In this way, the rotation curve w = w(R) and the corresponding velocity curve V = V(R) (= wR) are obtained.

Figure 17.19 shows the rotation curve of the Milky Way. Its central part rotates like a rigid body, i. e. the

Fig. 17.19. Rotation curve of the Milky Way based on the motions of hydrogen clouds. Each point represents one cloud. The thick line represents the rotation curve determined by Maarten Schmidt in 1965. If all mass were concentrated within the radius 20kpc, the curve would continue according to Kepler's third law (broken line). The rotation curve determined by Leo Blitz on the basis of more recent observations begins to rise again at 12 kpc

angular velocity is independent of the radius. Outside this region, the velocity first drops and then begins to rise gradually. A maximum velocity is reached at about 8 kpc from the centre. Near the Sun, about 8.5 kpc from the centre, the rotational velocity is about 220 km s-1. According to earlier opinions, the velocity continues to decrease outwards. This would mean that most of the mass is inside the solar radius. This mass could then be determined from Kepler's third law. According to (6.34),

Using the values R0 = 8.5 kpc and V0 = 220 km s one obtains

M = 1.9 x 1041 kg = 1.0 x 1011 Mc

The escape velocity at radius R is I2GM

such stars would exceed the escape velocity. This has been confirmed by observations.

The preceding considerations have been based on the assumption that near the Sun, the whole mass of the Galaxy can be taken to be concentrated in a central point. If this were true, the rotation curve should be of the Keplerian form, V a R_1/2. That this is not the case can be established from the values of the Oort constants.

The derivative of the Keplerian relation

Using the properties (17.15) and (17.16) of the Oort constants, one finds

This gives an escape velocity near the Sun Ve = 310kms-1. One therefore should not see many stars moving in the direction of galactic rotation, l = 90°, with velocities larger than 90kms-1 with respect to the local standard of rest, since the velocity of for a Keplerian rotation curve. This disagrees with the observed value and thus the assumed Keplerian law does not apply.

The mass distribution in the Milky Way can be studied on the basis of the rotation curve. One looks for

17.4 Structural Components of the Milky Way

a suitable mass distribution, such that the correct rotation curve is reproduced. Recently distant globular clusters have been discovered, showing that the Milky Way is larger than expected. Also, observations of the rotation curve outside the solar circle suggest that the rotational velocity might begin to rise again. These results suggest that the mass of the Galaxy might be as much as ten times larger than had been thought.

## Why Does The Milky Way Rotate?

We live in a galaxy that is called the Milky Way. It’s called a barred spiral galaxy, which means that it has a spiral shape with a bar of stars across its middle. The galaxy is rather huge — at least 100,000 light-years in diameter, making it the second-biggest in our Local Group of galaxies.

More mind-blowing is that this mass of stars, gas, planets and other objects are all spinning. Just like a pinwheel. It’s spinning at 270 kilometers per second (168 miles per second) and takes about 200 million years to complete one rotation, according to the National Radio Astronomy Observatory. But why? More details below.

It’s worth taking a quick detour to talk about how long it takes the Solar System to move around the center of the galaxy. According to National Geographic, that’s about 225 million years. Dinosaurs were starting to arise the last time we were in the position we are today.

Scientists have mapped the spin using the Very Large Baseline Array, a set of radio telescopes. They examined spots where stars were forming and paid particular attention to those areas where gas molecules enhance radio emission, according to the National Radio Astronomy Observatory. Dubbed “cosmic masers”, these areas shine brightly in radio waves.

As Earth moves in its orbit, the shift of these molecules can be mapped against more distant objects. Measuring this shift shows how the entire galaxy rotates — and can even provide information about the mass of the Milky Way. So that’s all very neat, but why is it rotating in the first place?

If we think back to the early Universe, there are two big assumptions astronomers make, according to How Stuff Works: there was a lot of hydrogen and helium, with some parts denser than other areas. In the denser areas, gas clumped together in protogalactic clouds the thickest areas collapsed into stars.

In this image from the Wide Field Imager on the MPG/ESO 2.2-metre telescope at ESO’s La Silla Observatory in Chile young stars huddle together against a backdrop of clouds of glowing gas and lanes of dust. The star cluster, known as NGC 3293, would have been just a cloud of gas and dust itself about ten million years ago, but as stars began to form it became the bright group we see here. Clusters like this are celestial laboratories that allow astronomers to learn more about how stars evolve. Image Credit: ESO/G. Beccari

“These stars burned out quickly and became globular clusters, but gravity continued to collapse the clouds,” How Stuff Works wrote. “As the clouds collapsed, they formed rotating disks. The rotating disks attracted more gas and dust with gravity and formed galactic disks. Inside the galactic disk, new stars formed. What remained on the outskirts of the original cloud were globular clusters and the halo composed of gas, dust and dark matter.”

A simpler way to think about this is if you’re creating a pizza by tossing a ball of dough into the air. The spin of the dough creates a flat disc — just like what you observe in more complicated form in the Milky Way, not to mention other galaxies.

For more on the Milky Way, visit the rest of our section here in the Guide to Space or listen to Astronomy Cast: Episode 99.

## Up the Milky Way

Note - we might have this discussion any time during the sky tour, whenever it comes up.

You can see the Milky Way on any clear summer night, but up in the north woods, on especially clear nights, the Milky Way glows like a neon light, from north horizon to south horizon, brilliantly reflected in the lake by our camp. Most people recognize the Milky Way as a band of light across the night sky, but what is that band of light - where does it come from?

You'll see a similar phenomenon later when you look at the M13 globular cluster in Hercules. Through binoculars you will see it as a hazy patch. When you see it through a telescope - that is, closer up - you can pick out individual stars. The better the telescope, the 'closer' you can get to M13, the more stars you can see.

The star that is about halfway between Aquila's eastern wingtip and his body is called h (Eta) Aquilae -- and this is another Cepheid variable with a cycle of about 7 days. At its brightest it's nearly as bright as the body star, d (Delta) Aquilae (actually it's as bright as the eastern Pilot Star b Aquilae), and at its dimmest it's about as bright as i (Iota) Aquilae. This is one of only three Cepheids you can see by eye - you already met d Cephei, the original, and the third one is in the winter constellation of Gemini.

Deneb is the star at the tail of the Swan. Notice that it is about as bright as Altair, which is 16 light years away -- so how far would you guess Deneb is? As it happens. Deneb is 2600 light years away - about 150 times farther!! Deneb is actually 20,000 times brighter than Altair and 200,000 times brighter than our sun. If Deneb were as close as Altair, it would be visible in broad daylight and would cast a shadow at night. This star is one of the greatest super-giant stars known.

Notice in the picture above that Altair and Deneb are two of the three bright stars overhead, which form the "Summer Triangle". You will be introduced to the third (Vega) in just a moment.

Albireo, the star at the head of the swan, is actually a beautiful double star, a yellow giant and a blue main-sequence star. You can just split this star with good binoculars held steady, and it looks better in a telescope.

Note that you can see how this all lays out, looking down on the galaxy, in the latest Milky Way diagram to come from NASA, based on new Spitzer Telescope observations.

If you locate the two tail-feather stars of Sagitta in binoculars then follow the line between them up (to the northwest), just one field of view, you will see the Coathanger, an interesting cluster of stars.

If you are really good with those binoculars you can go up from the tip of the arrow, toward Albireo in Cygnus, and you will find a group of stars that just fill the field of view in the shape of an "M". Right at the central point of the "M" is a faint fuzzy patch that actually is known as the "Dumbbell Nebula". To really see its hourglass shape requires a telescope. This hazy patch once was a star, until it blew itself apart.

This is called a "planetary nebula", because the typical disk shape (this one is less typical) suggested the look of a planet to early astronomers. In fact it has nothing to do with planets at all. This is what's left of a red giant star that finally did what all red giants eventually do. When the fuel at the core runs so low that the nuclear reactions can no longer hold up the weight of the star, it all collapses in to the center, which in turn raises the temperature so high that the star blows off its outer envelope of gases, losing much of its mass. This exposes the core to outer space, or, more accurately, exposes outer space to the core. The intense radiation from the core causes the expanding shell of gas to light up like a neon light, and voila -- the faintly glowing dumbbell that you see here. The white-hot core of this star is now a "white dwarf" -- on some planetaries you can see the star at the center. The Dumbbell's central star is notoriously elusive, though, and we probably can't see it in our telescope.

So diffuse nebulae, like the two we saw in Sagittarius, are the birthplaces of many new stars, and a planetary nebula is the deathbed of a single dying star. We will see another, even more famous, planetary nebula in the next constellation.

## Why does the Milky Way rotate?

The Milky Way is a spiral galaxy with several prominent arms containing stellar nurseries swathed in pink clouds of hydrogen gas. The sun is shown near the bottom in the Orion Spur. Credit: NASA

We live in a galaxy that is called the Milky Way. It's called a barred spiral galaxy, which means that it has a spiral shape with a bar of stars across its middle. The galaxy is rather huge—at least 100,000 light-years in diameter, making it the second-biggest in our Local Group of galaxies.

More mind-blowing is that this mass of stars, gas, planets and other objects are all spinning. Just like a pinwheel. It's spinning at 270 kilometers per second (168 miles per second) and takes about 200 million years to complete one rotation, according to the National Radio Astronomy Observatory. But why? More details below.

It's worth taking a quick detour to talk about how long it takes the Solar System to move around the center of the galaxy. According to National Geographic, that's about 225 million years. Dinosaurs were starting to arise the last time we were in the position we are today.

Scientists have mapped the spin using the Very Large Baseline Array, a set of radio telescopes. They examined spots where stars were forming and paid particular attention to those areas where gas molecules enhance radio emission, according to the National Radio Astronomy Observatory. Dubbed "cosmic masers", these areas shine brightly in radio waves.

As Earth moves in its orbit, the shift of these molecules can be mapped against more distant objects. Measuring this shift shows how the entire galaxy rotates—and can even provide information about the mass of the Milky Way. So that's all very neat, but why is it rotating in the first place?

If we think back to the early Universe, there are two big assumptions astronomers make, according to How Stuff Works: there was a lot of hydrogen and helium, with some parts denser than other areas. In the denser areas, gas clumped together in protogalactic clouds the thickest areas collapsed into stars.

The rising Milky Way at Sentosa Island in Singapore. Credit and copyright: Justin Ng.

"These stars burned out quickly and became globular clusters, but gravity continued to collapse the clouds," How Stuff Works wrote. "As the clouds collapsed, they formed rotating disks. The rotating disks attracted more gas and dust with gravity and formed galactic disks. Inside the galactic disk, new stars formed. What remained on the outskirts of the original cloud were globular clusters and the halo composed of gas, dust and dark matter."

A simpler way to think about this is if you're creating a pizza by tossing a ball of dough into the air. The spin of the dough creates a flat disc—just like what you observe in more complicated form in the Milky Way, not to mention other galaxies.

In this image from the Wide Field Imager on the MPG/ESO 2.2-metre telescope at ESO’s La Silla Observatory in Chile young stars huddle together against a backdrop of clouds of glowing gas and lanes of dust. The star cluster, known as NGC 3293, would have been just a cloud of gas and dust itself about ten million years ago, but as stars began to form it became the bright group we see here. Clusters like this are celestial laboratories that allow astronomers to learn more about how stars evolve. Credit: ESO/G. Beccari

## How Do You Set Up Astrotracer?

Astrotracer is a simple feature to use on the Pentax K-1 and K-1 II. But there are still a few steps involved to set up your camera correctly to use it.

Turn your camera on, set your camera to “Bulb” mode, and calibrate the camera’s GPS. BEFORE you start calibrating the in-camera GPS on the K-1, K-1ii, or K-3ii, there are a few things you need to keep in mind.

Large metal objects like cars, gazebos, or metal buildings can interfere with your GPS calibration. Being near them may result in a miscalibration.

Your phone’s signal, signals from some wireless shutter releases, and heavily-populated areas with many phones and power lines can also interfere with the GPS calibration.

Also, you can sometimes have issues with getting a proper calibration if shooting from inside washes, canyons, or ravines. The GPS calibration is best done in an open area away from vehicles, buildings, and heavily-populated areas.

### Step 1

Start by pressing the GPS button on the top of the camera next to the smart dial an orange light next to the button will indicate the GPS is on.

The orange LED next to the GPS button indicates it is on.

### Step 2

Go to the K-1’s “Settings 2” menu and select the “GPS/Electronic Compass,” menu item.

Select “GPS/Electronic Compass,” from the K-1 menu.

### Step 3

Select “Calibration” and follow the on-screen instructions. It tells you to rotate your camera on three different axes at least 180 degrees.

Follow the on-screen illustration to calibrate the GPS.

You should see a “Calibration Complete” notification once you’ve successfully calibrated your GPS. If the calibration is unsuccessful, then try walking around. Move a few feet in different directions or waiting a minute for a possible better signal. I have successfully calibrated my GPS in one try but have also failed to calibrate it several times in one night.

“Calibration Complete” shows the GPS is ready to use.

NOTE: Under the Camera 3 > Astrotracer menu, you can also perform a precise calibration to make Astrotracer more accurate when tracking the sky.

By performing the precise calibrations, you will be able to shoot easily with some telephoto or super-telephoto lenses with ease.

### Step 4

Check to make sure you have a GPS signal. You will see a small GPS signal indicator. It looks like a satellite on the top of your settings or live-view screen when your GPS is on. Once it turns green, you’re ready to shoot.

A green satellite icon at the top of the screen (left image) shows the Pentax K-1 has successfully locked onto the GPS signal.

### Step 5

The last step is to turn on Astrotracer.

When your camera is in live view mode or displaying camera settings, you can press the “Info” button on the back of the camera to go to a grid of icons. One is the Astrotracer icon, which looks like a shooting star with a square box “reticle” surrounding the star.

The Pentax Astrotracer is ready to use.

Once you turn Astrotracer on, you’re ready to shoot tracked images.

## Speed of the Milky Way in Space

As we all know, a galaxy is a massive ensemble of hundreds of millions of stars. The galaxy where we live in today is called the Milky Way. The name itself came from the ancient Greek galaxies kyklos, or ring of milk, due to its faint milky appearance. Our Milky Way is a large spiral galaxy. Its diameter is at least 100,000 light-years, and may contain as many as 200 billions stars today.

Ever since four hundred years ago the settlement that the Earth is moving about the sun, and one hundred and fifty years ago that the sun is moving about the center of the Galaxy, it shouldn't be surprising if we learned that the Galaxy is also moving. The Milky Way is part of a cluster of galaxies call the Local Group. Two chief members are the Milky Way and the Andromeda galaxy, the Andromeda galaxy is known to contain at least 300 billion stars. We can presume that in every cluster of galaxies, the individual galaxy itself move about some sort of center of gravity. However, how do the clusters themselves move?

In 1928, an American astronomer Milton La Salle Humason found a galaxy that was receding at a speed of 3,800 km/s, and by 1936, when he observed the same galaxy again, he found it receding at a speed of 40,000 km/s. It didn't make any sense that the galaxies be receding from us and yet the recessions would be faster as they get farther way from each other. "Was there something special about our galaxy? Did it repel other galaxies, and did this repulsion grow stronger with distance?

If our galaxy exerted a repulsive force, that force should be felt with the local groups, however it wasn't. Furthermore, a repulsive force that grew stronger with distance is highly unlikely. For example, as we've learned in the past, a magnetic pole can repel another magnetic pole like itself, and an electric charge can repel another electric charge like itself, but in each of the cases, the repulsion weakens with the increase of distance. Hubble, an American astronomer, concluded in 1929 that the "entire universe was steadily expanding"and that the galaxies were moving apart from one another as part of this expansion and not because of any repulsive force. In addition, in 1916, Albert Einstein as part of his general theory of relativity, had prepared a set of equations that were intended to describe the properties of the universe as a whole, that showed that the universe would have to be expanding.

In conclusion, galaxies experience neutral attractions on one other. Due to relativity, the speed of the Milky Way varies when compared with different objects in space. For example, I have learned from my research that the Milky Way and Andromeda galaxy are approaching each other with a speed of about 130 km/s, however the collision of these two galaxies will not occur for about 5 billion years (AstroFile). Another result I found was that our galaxy and neighbors are moving at 600 km/s in the direction of the constellation Hydra (Scientific American). Finally, I found that the Milky Way moves through space within the cluster of galaxies it is a member of, and this cluster in turn moves through space towards yet another larger cluster of galaxies off in the direction of the constellation Virgo. This speed is approximately 300 km/s (Ask the Space Scientist). Therefore, the speed of the Milky Way galaxy is not a single number, its value is relative to the speed of other objects.

Bibliographic Entry Result
(w/surrounding text)
Standardized
Result
Hall, Stephen S. Mapping the Next Millennium. New York: Random House: 1992, 328, 334. "The Great Attractor is … incredibly dense and unimaginably large, lying off at a distance of 150 million light years, in the direction of the Hydra Centaurus supercluster …. Our galaxy, the Milky Way, is caught in the tug of this Great Attractor, and so are we, hurtling -- though we'd never know it -- toward this mysterious mass at a speed of 370 miles per second." 600 km/s
"That exact fate befell Vera Rubin and W. Kent Ford, Jr., of the Carnegie Institution of Washington and two colleagues in the mid-1970s. Using complicated and (to hear some astronomers tell it) not entirely convincing measurements, they reported that the Milky Way, our galaxy, had a peculiar velocity of about 500 kilometers per second. In other words, the Milky Way was hurtling about 370 miles per second off the plumb of the big bang. Rubin in fact had suggested the same thing way back in 1950, but her data had been even sketchier, the reaction even chillier." 600 km/s
Rhett Herman, How Fast is the Earth Moving? Scientific American: Ask the Experts. 26 October 1998 "The galaxies in our neighborhood are also rushing at a speed of nearly 1,000 kilometers per second towards a structure called the Great Attractor, a region of space roughly 150 million light-years (one light year is about six trillion miles) away from us. This Great Attractor, having a mass 100 quadrillion times greater than our sun and span of 500 million light-years, is made of both the visible matter that we can see along with the so-called dark matter that we cannot see." 1,000 km/s

The motion of galaxies is determined from an apparent change in the color of light they emit. There are gaps within the spectra of the light emerging from every galaxy. These gaps, called absorption lines, are not located in the spectra at random. The patterns in the missing wavelengths tell us something about the elements present in the stars. In a sense, spectra are like fingerprints. Each element has its own specific set of absorption lines. When a star or group of stars (which is what a galaxy is) are moving relative to us on earth, these elemental fingerprints get shifted from their usual location in the spectra. When a galaxy is moving towards us, these fingerprints get shifted toward the blue end of the spectrum and when a galaxy is moving away from us, they get shifted toward the red end. The amount of shift can be used to determine speed. The greater the shift, the faster the galaxy is moving relative to us on earth.

This phenomena is an example of the Doppler effect -- an apparent change in the frequency of a wave when either the source or observer of the wave are moving -- named for the Austrian physicist Christian Döppler who first described it in the 1840s. The Doppler effect is familiar to anyone who has heard a horn or siren sounding while it went past them. As the horn approaches the listener it has one sound -- a pitch that's higher than normal (although most people are unaware of this). When the horn passes it has another sound -- one that's obviously lower in pitch (and that most people notice). The Doppler effect is used to measure the speed of many things: baseball pitches, tennis serves, speeding cars, and blowing rain (thus the name, Doppler radar).

Of the billions of galaxies in the observable universe, nearly all of them have spectra with a red shift that is, they are moving away from us. Moreover, the degree of red shift, and thus the speed, of the galaxies in the universe is very nearly directly proportional to their distance from the Milky Way (an observation first reported by the American astronomer Edwin Hubble in the 1920s). This is generally interpreted as evidence for the overall expansion of the universe. It's not that the galaxies are rushing away from us. Rather, it's that the very space between them is getting larger. They aren't moving, nor are we. The universe is just getting larger and we happen to be in the universe.

Note that I wrote that the speed of the galaxies in the universe is very nearly directly proportional to their distance from us. Superimposed on the "recessional velocity"associated with the expansion of the universe is a "peculiar velocity"associated with the individual wandering motions of galaxies. If you imaging being on a train with a group of people, the recessional velocity is something like the motion of the train as a whole, while the peculiar velocity is something like the motion of the passengers milling about within the car. The first is a global property while the second is a local property, although "local"in this sense is hardly "small".

These peculiar velocities were always assumed to be randomly distributed since it was always assumed that the universe was homogeneous that is, well mixed with no lumps or pockets. In the 1980s, astronomers began systematically cataloging the location and peculiar velocities of thousands and then millions of galaxies. What they found was the opposite of the assumption: the universe is not well mixed and the peculiar velocities are not randomly distributed. The universe isn't creamy, it's foamy like a collection of bubbles, with galaxies being the "liquid"web that surrounds the "bubbles"of empty space. The galaxies aren't wandering, they're going somewhere not all of them, but certainly several million of them in the space around the Milky Way.

In 1987, a group of seven astronomers uncovered this coordinated motion of the Milky Way and our several million nearest galactic neighbors -- Alan Dressler, Sandra Moore Faber, Donald Lynden-Bell, Roberto Terlevich, Roger Davies, Gary Wegner and David Burstein. Their results were so astounding they acquired the equally astounding nickname of "The Seven Samurai"(the name of a classic Japanese Samurai movie that spawned the classic American Western movie "The Magnificent Seven"). The place towards which we all appear headed was originally called the New Supergalactic Center or the Very Massive Object until one of the discoverers, Alan Dressler, decided they needed a catchier name and came up with "The Great Attractor".

The mass of the Great Attractor truly is great. Whereas our galaxy contains the equivalent of 10 11 solar masses, the Great attractor is estimated to be on the scale of 10 17 solar masses a million times heavier than the Milky Way. If the Milky Way were a piece of gravel, the Great Attractor would be a truck. It's attraction is so strong that we are being sucked into it at the rate of 600 km/s. In comparison, the earth moves around the sun at the relatively pokey rate of 30 km/s and rockets escaping the earth's gravitational pull barely move at 11 km/s.

The Great Attractor is something on the order of 150 million light years from earth. One light year is the distance a ray of light would travel in the vacuum of space in one year -- about 10 13 km. At the rate stated, we should arrive at the center of the Great Attractor in something like 15 billion years. Those of you who can't wait will be pleased to know that this is the upper limit on the estimated time of arrival. Since forces accelerate objects we will surely arrive there a few billion years earlier.

What we will find there remains uncertain. Pictures of the Great Attractor are hard to come by as this region in the sky is obscured by the dust and debris of our own galaxy. We can see where these millions of galaxies are headed, but we don't know what's there. Infrared images have revealed galaxies clustered at the center of the attractor, but they contain nowhere near the mass predicted by calculations. The problem of missing mass is one that is now common in astronomy. The large scale structure and behavior of the universe just can't be explained in terms of the mass that is visible to astronomers. Candidates to fill the vacancy include such bizarre entities as MACHOs (massive compact halo objects), WIMPs (weakly interacting massive particles), and other forms of so-called "dark matter". I have to put dark matter in quotes, because I think it's a terrible name. Dark matter is not dark or black, if it were somebody would have seen it, or rather somebody would have noticed a patch of sky that had nothing in it. Dark matter would better be called "invisible matter"as it doesn't interact with photons (the particles that make up visible light). Whatever the case, explaining away the missing matter -- explaining what it is that makes up the heart of the Great Attractor -- will surely rank as one of the greatest discoveries in the history of science.

## Galaxies

Understanding what our galaxy looks like is difficult as it is like making a drawing of your house if you have only ever been on the inside and never seen it from outside. We notice a few things from other galaxies that give us clues.

There is a plane, or disc about 1,500 light years thick. There are spiral arms that make up this plane.

The plane from one end to another is between 100,000 to 150,000 light years across.

Also there is a central bulge in the centre. This is in the region of Sagittarius, but we cannot see it very well because there is a lot of cosmic dust in the way. We can however detect it with infrared and radio signals.

At its centre is believed to be a supermassive black hole called Sagittarius A which is a source of immense radiation which we can detect.

##### Sun Location

The Sun is around 30,000 light years from the centre of the Milky Way. This is about two-thirds of the way from the centre, along one of the spiral arms.

Like the planets orbiting the Sun, the Sun in turn orbits the centre of the Milky Way along a spiral arm.

It takes 226 million years to make a galactic orbit.

The Sun is positioned on a spiral arm called the Orion Arm.

##### Other Locations

Dust: Dark bands between the solar system and the centre of the galaxy are caused by dust clouds known as the great rift. Spiral arms contain a large amount of interstellar gas and dust.

Globular clusters: These are the oldest objects in the milky way and surround the halo - the dusty area around the galaxy. Star clusters are positioned near the arms.

Star formation: Takes place in the disk and spiral arms as gas and dust is dense and cool enough to form stars.

##### Rotation

It is more accurate to study the rotation of our galaxy by radio waves because we can only see part of the sky with visible light.

The 21cm (centimetre) range is known as the Hydrogen line which allows us to see past clouds of interstellar cosmic gas and dust. The centre of the galaxy has a lot of this. It has told us the structure and rotation of the galaxy.

##### Type of Galaxy

The Milky Way is an Sb (Spiral barred) galaxy. Until recently it was considered a spiral galaxy.

## Massive investigation

The primary way astronomers estimate stars in a galaxy is by determining the galaxy's mass. The mass is estimated by looking at how the galaxy rotates, as well as its spectrum using spectroscopy.

All galaxies are moving away from each other, and their light is shifted to the red end of the spectrum because this stretches out the light's wavelengths. This is called "redshift." In a rotating galaxy, however, there will be a portion that is more "blueshifted" because that portion is slightly moving toward Earth. Astronomers must also know what the inclination or orientation of the galaxy is before making an estimate, which is sometimes simply an "educated guess," Kornreich said.

A technique called "long-slit spectroscopy" is best for performing this type of work. Here, an elongated object such as a galaxy is viewed through an elongated slit, and the light is refracted using a device such as a prism. This breaks out the colors of the stars into the colors of the rainbow.

Some of those colors will be missing, displaying the same "patterns" of missing portions as certain elements of the periodic table. This lets astronomers figure out what elements are in the stars. Each type of star has a unique chemical fingerprint that would show up in telescopes. (This is the basis of the OBAFGKM sequence astronomers use to distinguish between types of stars.)

Any kind of telescope can do this sort of spectroscopy work. Kornreich often uses the 200-inch telescope at the Palomar Observatory at the California Institute of Technology, but he added that almost any telescope of sufficient size would be adequate.

The ideal would be using a telescope in orbit because scattering occurs in Earth's atmosphere from light pollution and also from natural events &mdash even something as simple as a sunset. The Hubble Space Telescope is one observatory known for this sort of work, Kornreich added. A successor observatory called the James Webb Space Telescope is expected to launch in 2020. The challenge, however, is that Hubble is a telescope in high demand &ndash and the same is expected of Webb after its launch. So the observatories can't spend all of their time estimating galaxy mass.

## How many times has the Milky Way rotated? - Astronomy

The stars and gas and dust clouds in the disk congregate in a spiral pattern. There are four parts to the spiral pattern in our Galaxy called spiral arms. There are many stars that are also in-between the spiral arms, but they tend to be the dimmer stars (G, K, M-type stars). Long-lived stars will move in and out of the spiral arms as they orbit the galaxy. Star formation occurs in the spiral arms because the gas clouds are compressed in the arms to form stars. The very luminous, short-lived O and B-stars and H II regions around them enhance the spiral outline. They outline the spiral pattern the same way Christmas lights around the edges of a house will outline the borders of the house at night. The O and B-type stars live for only a few million years, not long enough to move outside of a spiral arm. That is why they are found exclusively in the spiral arms.

Differential rotation provides an easy way to produce a spiral pattern in the disk. Differential rotation is the difference in the angular speeds of different parts of the galactic disk so stars closer to the center complete a greater fraction of their orbit in a given time. But differential rotation is too efficient in making the spiral arms. After only 500 million years, the arms should be so wound up that the structure disappears. Also, the spiral pattern should occupy only a small part of the disk. The observations of other galaxies contradicts this: the spiral arms in spiral galaxies rarely have more than two turns. Galaxies are billions of years old so the spiral pattern must be a long-lasting feature. What maintains the spiral pattern?

#### Density Wave Theory

In a galaxy the spiral region of greater gravity concentrates the stars and gas. The spiral regions rotate about as half as fast as the stars move. Stars behind the region of greater gravity are pulled forward into the region and speed up. Stars leaving the region of greater gravity are pulled backward and slow down. Gas entering spiral wave is compressed. On the downstream side of wave, there should be lots of H II regions (star formation regions). This is seen in some galaxies with prominent two-armed spiral patterns. But there are some unanswered questions. What forms the spiral wave in the first place? What maintains the wave?

#### Self-propagating Star Formation

Computer simulations of galaxy disks with a series of supernova explosions do produce spiral arms but they are ragged and not as symmetrical and full as seen in so-called grand-design'' spirals that have two arms. There are spiral galaxies with numerous, ragged spiral arms in their disks (called flocculent'' spirals), so perhaps the self-propagating star formation mechanism is responsible for the flocculent spirals.

## How many times has the Milky Way rotated? - Astronomy

About 99% of the interstellar medium is gas with about 90% of it in the form of hydrogen (atomic or molecular form), 10% helium, and traces of other elements. At visible wavelengths, however, dust has a greater effect on the light than the gas. The presence of interstellar gas can be seen when you look at the spectral lines of a binary star system. Among the broad lines that shift as the two stars orbit each other, you see narrow lines that do not move. The narrow lines are from much colder gas in the interstellar medium between us and the binary system.

The hydrogen gas is observed in a variety of states: in ionized, neutral atomic, and molecular forms. The ionized hydrogen emits light in the visible band as the electrons recombine with the protons and the neutral atomic and molecular hydrogen emits light in the radio band of the electromagnetic spectrum.

#### H II Regions

Below is a famous H II region called the Orion Nebula. It is the fuzzy patch you can see in the sword part of the Orion constellation. It is the closest large star formation factory to us and is explored in more detail in the stellar evolution chapter. Selecting the image will bring up a close-up of the heart of the nebula in another window showing the four hot "Trapezium" stars (four O and B stars making a trapezoid figure) at the center of each of the images by AAO and HST.

Another large H II region is the Lagoon Nebula in the constellation Sagittarius. It is about 5000 light years away and spans 90 by 40 arc minutes in our sky. Converting the angular size to a linear size, the Lagoon Nebula is about 130 by 60 light years in extent (the Orion Nebula is only 29 by 26 light years in size). The complex interaction of the intense radiation from the hot stars lighting up the nebula, varying densities of the gas and dust, and temperature differences creates twisted, turbulent features in the nebula that have been explored by the Hubble Space Telescope. Selecting the image will bring up the high-resolution image of the heart of the Lagoon Nebula from the Hubble Space Telescope in another window.

Next to the Lagoon Nebula on our sky (but closer to us in space) is the Trifid Nebula, so-called because of the dust lanes that trisect the H II region behind them. The image below is nice one to illustrate the three types of nebulae: the red H II region behind a dark dust nebula (showing the effect of the extinction of light) and next to them a blue reflection nebula (showing the preferential scattering of shorter wavelengths).

O and B-type stars are only found in regions of star formation because they are young stars. These hot, very luminous stars do not live long enough to move away from where they were formed. Since stars form in clusters, where O and B stars are found, there are sure to be smaller, lower-mass stars still forming. The spectra of H II regions are much simpler than star spectra so they are easier to decipher. The composition and conditions inside the H II regions are easier to determine and understand than for stars, so H II regions provide a valuable tool for understanding the history of star formation in a galaxy.

H II regions also provide a convenient way to map the structure of a galaxy because they are so large and luminous. In our galaxy the H II regions are distributed in a spiral pattern. The best wavelengths to use to map the distribution of hydrogen, however, are in the radio band. Most of the hydrogen gas is not ionized because O and B stars are rare. Also, energy in the form of radio passes easily through dust.

Most of the hydrogen in space (far from hot O and B-type stars) is in the ground state. The electron moving around the proton can have a spin in the same direction as the proton's spin (i.e., parallel) or spin in the direct opposite direction as the proton's spin (i.e., anti-parallel). The energy state of an electron spinning anti-parallel is slightly lower than the energy state of a parallel-spin electron. Remember that the atom always wants to be in the lowest energy state possible, so the electron will eventually flip to the anti-parallel spin direction if it was somehow knocked to the parallel spin direction. The energy difference is very small, so a hydrogen atom can wait on average a few million years before it undergoes this transition.

Even though this is a RARE transition, the large amount of hydrogen gas means that enough hydrogen atoms are emitting the 21-cm line radiation at any one given time to be easily detected with radio telescopes. Our galaxy, the Milky Way, has about 3 billion solar masses of H I gas with about 70% of it further out in the Galaxy than the Sun. Most of the H I gas is in disk component of our galaxy and is located within 720 light years from the midplane of the disk. What's very nice is that 21-cm line radiation is not blocked by dust! The 21-cm line radiation provides the best way to map the structure of the Galaxy.

#### Using 21-cm line radiation to Map the Galaxy

The rotation curve is a plot of the orbital velocity of the clouds around the galactic center vs. their distance from the Galaxy center. The term "rotation" in this context refers to the motion of the galactic disk as a whole---the disk made of stars and gas clouds appears to spin. The gas clouds are assumed to move in the plane of the disk on nearly circular orbits. Jan Oort (lived 1900--1992) found in 1927 that stars closer to the galactic center complete a greater fraction of their orbit in a given time than stars farther out from the center. This difference in the angular speeds of different parts of the galactic disk is called differential rotation.

The rotation curve can be determined by looking at the doppler velocities of hydrogen gas along different lines of sight. The 21-cm emission will include contributions of hydrogen at different distances from the galactic center and different doppler shifts with respect to us. Some of the emission will be from gas clouds just inside the orbit the orbit of the Sun moving at slightly faster angular speeds than the Sun. They will have a small redshift. The part of the total emission coming from gas closest to the galactic center will have the greatest redshift because that gas is moving at the greatest angular speed. In the figure below the line from the galactic center to the fast moving gas (called "Rmin" ) makes a 90° angle with respect to our line of sight. Using basic trigonometry, the distance of the fast moving gas (at "A" ) from the galactic center = (the Sun's distance)× sin[(galactic longitude)], where the galactic longitude is the angular separation between the cloud and the galactic center and sin() is the "trigonometric sine" function (it is the "sin" key on a scientific calculator). Angle by angle, strip by strip, the rotation curve is constructed from the maximum doppler velocity along different lines of sight. Among the highest resolution HI maps of the entire sky, the HI4PI survey released in late 2016, required more than a million observations over thousands of hours and the processing of ten billion data points over several years.

Once the rotation curve is determined, the Galaxy's structure can be mapped. The 21-cm line profile has several doppler shifted peaks that are narrow and well-defined (see the figure below). Using the known rotation curve, you can convert the doppler speeds of the peaks to get the distance to the hydrogen producing each peak. The intensity of each peak depends on the density of the hydrogen gas cloud. The mapping surveys show that the hydrogen gas is distributed in a spiral pattern in a thin disk for almost all of the Galaxy. At a Chautauqua short course on radio astronomy at Green Bank, two classmates and I used this technique to see if we could detect the newly-discovered outer arm of the Milky Way with the 40-foot radio telescope. To read more about our test, see my "Day-5 Chautauqua 2011" report.

Two illustrations of the Milky Way as seen face-on are shown below. The left (top) is from Diana Marques and the right (bottom) is from National Geographic. Select the left image to go to Kevin Jardine's "Galaxy Map" site that goes into more details about mapping the Galaxy.

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#### Molecules

Based primarily on observations of the CO emission, astronomers find that the molecules in the interstellar medium are clumped together into clouds with masses anywhere from just a few solar masses to over a million solar masses with diameters ranging from several light years to over 600 light years. Molecules need to have some sort of shielding from the high-energy light from stars. Otherwise, the energetic photons would dissociate the molecules. Molecular clouds have dust in them. The dust grains may provide the shelter for molecules to form. Compared to the size of atoms, the dust grains are enormous and have many pits and recesses for atoms to congregate and combine.

Stars form in the molecular clouds. If the molecular cloud is cold and dense enough, it can collapse under its own gravity. Smaller fragments can form and produce stars (see the stellar evolution chapter for further details). The Milky Way has about 2.5 billion solar masses of molecular gas with about 70% of it in a ring extending from 13,000 to 26,000 light years from the center. Not much molecular gas is located at 4,900 to 9,800 light years from the center but about 15% of the total molecular gas mass is located within 4,900 light years from the center. Most of the molecular clouds are clumped in the spiral arms of the disk and stay within 390 light years of the disk mid-plane.

Molecular hydrogen H2 does not produce radio emission. It produces absorption lines in the ultraviolet. However, the gas and dust become so thick in a molecular cloud that the ultraviolet extinction is too large to accurately measure all of the H2 in the interior of the cloud. Fortunately, there is evidence of a correlation between the amount of CO and H2, so the easily detected CO radio emission lines (at 2.6 and 1.3 mm) are used to infer the amount of H2. The CO emission is caused by H2 molecules colliding with the CO molecules. An increase in the density of the H2 gas results in more collisions with the CO molecules and an increase in the CO emission.

Another nice feature of the CO radio emission is that its wavelength is small enough (about 100 times smaller than 21-cm line radiation) that even medium-sized radio telescopes have sufficient resolution to map the distribution of the molecular clouds. The higher resolution of large radio telescopes can be used to probe the structure of individual molecular clouds. There is some controversy about how the molecules are clumped together in the clouds. Is one gas cloud actually made of many smaller gas clouds? There is some evidence that indicates that 90% of the H2 is locked up in 5000 giant molecular clouds with masses greater than 10 5 solar masses and diameters greater than 65 light years. The largest ones, with diameters greater than 160 light years, have more than a million solar masses and make up 50% of the total molecular mass. Other studies indicate that the giants are actually made of smaller clouds grouped together into larger complexes.