Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
First observation of gravitational waves wikipedia , lookup
Gravitational lens wikipedia , lookup
Main sequence wikipedia , lookup
Stellar evolution wikipedia , lookup
Accretion disk wikipedia , lookup
Cosmic distance ladder wikipedia , lookup
Astronomical spectroscopy wikipedia , lookup
Wednesday, November 27, 2004 Please come to the front of the room and take back your papers. If you absolutely cannot attend discussion on Nov. 24, then you may make it up by writing a one to two page paper (double spaced) on the Cassini Mission that has recently arrived at Saturn (http://saturn.jpl.nasa.gov). This should be handed in to me before the 24th. Late submissions will not be accepted. For details, see last week’s discussion notes online. Black Hole film You should be able to reproduce and label the pictures of the Milky Way Galaxy from different angles (ex. figure 14.1). Disk Stars Found in the disk Spend all of time in disk Orbit in same direction, bobbing up and down Halo Stars Found in or near the halo Spend most of time in halo Orbit in random directions Bulge Stars Found in bulge Spend all of time in bulge Orbit in random directions Measuring masses – finding dark matter! Remember how we could measure the mass of a binary system using Newton’s version of Kepler’s third law? To do so, we needed to know the period of the binary system and the distance between the two stars. In a similar way, we can determine the mass of the galaxy interior to the orbit of a star if we know the period of the star’s orbit about the galactic center and the distance between the star and the galactic center. For instance, we can carry out this calculation for our Sun. Recall that Newton’s version of Kepler’s third law is: 4 2 2 P a3 G( M 1 M 2 ) where P is the orbital period (in seconds), a is the average distance (in meters), M1 and M2 are the masses of the things being considered (in kilograms), and G is the gravitational constant. In this case, the things being considered are the entire Milky Way galaxy and the Sun. Therefore, a = the average distance between the sun and the galactic center, and P = the orbital period of the Sun about the galactic center. 9.46 1012 km 2.6488 1017 km 2.6488 1020 m a 28,000 light - years 1 light - year In the text, we are not given the Sun’s period, but we are given it’s velocity. To find the period from a and the velocity of 220 km/s: distance traveled 2πa 2π 2.6488 1017 km P 7.56496 1015 s velocity v 220 km/s Now plug into Newton’s version of Kepler’s third law and solve for mass: 7.56496 10 s 15 6.67 10 11 2 3 4 2 2.6488 10 20 m 11 3 2 6.67 10 m /kg s (M 1 M 2 ) m 3 /kg s 2 7.56496 1015 s 2 4 2 2.6488 10 20 m 3 1 (M 1 M 2 ) 4 2 2.6488 10 20 m 3 (M 1 M 2 ) 6.67 10 11 ( M 1 M 2 ) 2 10 41 kg m 3 /kg s 2 7.56496 1015 s 2 1.922 10 41 kg Why is it that this only tells us the mass of the material within the Sun’s orbit? Newton’s version of Kepler’s third law is based upon gravity. (If we had derived this law from basic physical principles rather than simply presenting it to you, this would be obvious. As it is, just trust me on this one.) The force of gravity from the material outside of the orbit is in all different directions, so it practically cancels out. The force of gravity from the material within the orbit is all in the same direction, so it adds up. We can, in theory, do similar calculations for stars that are closer to the edge of the disk to find the mass of a greater portion of the galaxy. Since the bulge looks so big and bright, we expect that most of the mass of the galaxy is located in the center. However, in order for this to be true the orbital periods of the stars closer to the edge of the disk would have to be larger (i.e. their velocities would have to be smaller.) Conversely, if most of the mass is in the halo, the orbital periods of the stars closer to the edge of the disk would have to be about the same as the stars near the bulge (i.e. their velocities would have to be about the same as the stars near the bulge.) Why, you ask? Well, you don’t REALLY need to know this for the course… but let’s take another look at Newton’s version of Kepler’s third law, slightly rewritten. 4 2 a 3 (M1 M 2 ) GP2 4 2 a 3 distance traveled G velocity 2 4 2 a 3 2πa G v 2 av 2 If most of the mass is located in the bulge, and you look at the total amount of mass within a disk star’s orbit, that total mass will not change much as you examine stars further and further away from the bulge. Your a is getting larger and larger, but the mass is not changing by much, so the only other variable, the period, must be increasing enough to counterbalance the increasing a. The period is dependent on the velocity, so if the period is increasing, then the velocity must be decreasing. Contrary to our expectations, stars that are far from the galactic center have velocities that are comparable to stars near the bulge. We explain this by saying that the bulk of the mass in our galaxy is not in our bulge, but in our halo. We call this mass “dark matter” because we do not detect it emitting light.