Exploring Our Universe: From the Classroom to Outer Space I. Spectroscopy Student Activity #7

One type of information astronomers are able to measure when they explore the universe with spectroscopy is the speed at which celestial objects are moving towards or away from us. They can do this by applying a principle called the Doppler Effect (named after the scientist who first described the effect).

The Doppler Effect consists of the fact that when a moving source emits a wave, the wavelength we measure is decreased when the source is moving towards us, compared to the wavelength we would measure if the source is at rest. Likewise, if the source of the wave is moving away from us, the wavelength we measure is increased.

The most common way people experience the Doppler Effect is when they listen to the sound of an ambulance siren as it passes by. When the ambulance is approaching, the pitch of the siren (meaning the "sharpness" or "lowness" of the tone you hear, not the loudness) is slightly higher than it would be if the ambulance were not moving. But the instant the ambulance passed by you, the pitch of the siren suddenly drops! This is because the ambulance is now moving away from you. As it moves away, the sound waves are stretched out over a greater distance, and their wavelength is increased. This increase in wavelength lowers the pitch of the sound we hear once the ambulance passes by. The same effect happens with light waves as with sound waves- only we can't hear light!

Light and the Doppler Effect

The Doppler Effect is also noticed when we observe light emitted by a source, such as a star or galaxy, that is moving away from or towards us. If the source of light is moving towards us, the wavelength of light we observe is decreased relative to what we would observe if the source were not moving. Scientists call this a "blue shift," since the effect was first observed in visible light, and blue light has shorter wavelengths than other visible light. If the source of light is moving away from us, the wavelength we measure is increased. This is known as a "red shift." The terms "blue shift" and "red shift" are slightly misleading, since the Doppler Effect can occur at any wavelength of light, not just in the visible range.

Consider the two spectra below. In fig. A, the spectral emissions are from hydrogen gas measured in a laboratory. Notice there is an emission line at 486 nanometers (nm). The lines in fig. B represent data collected by an astronomer, from a star, also containing hydrogen gas. In this case, the emission line that was at 486 nm has shifted to a lower wavelength, 483 nm. Each of the other four lines experience the same decrease in wavelength, compared with fig. A.

Fig.A

Fig. B

Is the data in fig. B "red shifted" or "blue shifted?" _____________

Based on the change in wavelength, what could the astronomer conclude about the motion of the star?
____________________________________________________________________________
____________________________________________________________________________

Astronomers use this principle to calculate the rate of motion for objects in space. They use a formula stating the relationship between the change in wavelength of the light an object emits and the speed at which the object is moving away from or towards us:

When astronomers observe a star or a galaxy using spectroscopy, the wavelengths of light they measure are either "blue-shifted" or "red-shifted." By measuring the change in wavelengths of light relative to what they would measure in a laboratory, they can use the formula above to calculate the relative speed of the object, moving either towards us or away from us.

What's at the Center of Galaxy M84?

In May 1997, astronomers using the Hubble Space Telescope examined a galaxy known as M84, in a region of the universe called the Virgo Cluster. The entire galaxy is enormous- about 100,000 light-years across! (Remember that a light-year is the distance light travels in one year, about 9.5 trillion kilometers- think how big the entire galaxy is!) The astronomers focused their telescope at the very center of the galaxy. This is just a tiny part of the entire galaxy, only (!!) 26 light-years across. They collected spectral data from the intergalactic dust and gas swirling around the galactic core. [See diagrams at http://oposite.stsci.edu/pubinfo/pr/97/12.html]

The image above (NASA credit) show a spectrum of the central region of M84. The zigzag feature measured by the spectrograph is an example of a red and a blue shift: the blue part (shorter wavelength) is from gas moving towards us; the red part (longer wavelength) is gas moving away from us. Measuring the change in wavelength, from the center of the spectrum, astronomters found out a speed of 400 Km/s, or 880,000 miles per hour! What could possibly make this gas move so fast?

Applying Newton's Universal Law of Gravitation

Why was Isaac Newton so intrigued by an apple falling from a tree? Because he imagined the Earth pulling the apple towards it. This led him to conceive the idea that every object in the universe exerts a force- called gravity- on any other object. This brilliant observation gave scientists a mathematical tool, one used not only to describe the behavior of events we see but also to predict events we cannot observe directly.

Consider the example of one object circling another at a constant speed, very much like the Earth traveling around the Sun:

Although the speed of the small object remains the same, its velocity is always changing. (Remember that velocity is a vector that indicates both speed and direction.) A change in velocity means that acceleration a is occurring:
(v_final - v_inital) / (t_final - t_inital) = a; or using calculus, dv / dt = a). In the case of circular motion, the acceleration vector is always directed toward the center of the circle, where the large object sits. Aceleration due to circular motion is called centripetal acceleration, and can be calculated using the following formula:

What causes this centripetal acceleration? It is due to the pull of gravity from the other object at the center of the circular orbit. The formula stating the force of gravity between two objects is known as Newton's Law of Universal Gravitation:

We can now use Newton's first law of motion (F = m * a) to state an equality:
the force produced by the centripetal acceleration of the moving object m is equal to gravitational force between m and M:

From this equality we can derive a formula for the speed of the circling object:

Notice that the speed has nothing to do with the mass m of the circling object itself; it depends only on the mass M at the center of the orbit and the distance r from the center.

See if you can derive the above formula for the speed of the circling object, using the equivalence between the force produced by centripetal acceleration and the gravitational force:

What if we knew the speed v, but wanted to find the mass M- how would you rearrange the equation above?

The Galaxy M84

Astronomers use the very same formula for the mass M, whose gravity is keeping another object moving in a circular orbit, to estimate the mass of whatever is in the center of the galaxy M84. To find the value they obtained, use the value of speed we calculated from the spectrum, the value for the Universal Gravitational Constant G, and the distance between the swirling gas and the galactic center. One light-year is equal to 9.5 trillion kilometers!

(Two hints for solving the problem: first, since you are working with very large numbers, it would be a good idea to use scientific notation. Second, pay careful attention to the units- make sure you're not using meters in one place and kilometers in another.)

Mass of M84's core = _______

Let's see if we can put your answer into perspective by comparing what's at the center of M84 with the masses of other objects. By doing the same sort of calculation, we know that:

The ratio MSun / MEarth tells us that the Sun is 300,000 times as massive as the Earth!

Let's compare the mass at the center of galaxy M84 with the mass of the Sun:

M_M84 / M_Sun = _________

This ratio should tell you that whatever is at the center of M84 is hundreds of millions times more massive than our Sun! Could this be possible? Is there anything in the universe that could swallow up a mass equivalent to millions and millions of stars into such a small volume?

What do you think could be at the center of M84? Explain why you think so.

____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________