Assignment: Kepler, Parallax and Magnitudes
1. Look at this animation of light traveling from Earth to the nearest star to our Sun (http://physics.bk.psu.edu/teaching/Univ6e/con_index.htm?99ann ), Proxima Centauri (it’s the first animation under Chapter I). On this scale, estimate where would the edge of the solar system would lie. How big would you have to blow up this illustration before you could realistically draw on where the edge of the solar system is with, say, a pencil?
2. In the far future we build a giant generation ship to make the trip to the Andromeda galaxy. It quickly accelerates up to 10% the speed of light, which is the speed it maintains for the rest of the journey. Estimate*: how long does it take to pass our nearest star? How long does it take to leave the Milky way galaxy? How long does it take to reach Andromeda? Show your working.
* In astronomy, typically when we estimate quantities we’re only interested in getting the answer to within a factor of a few. If a questions asks you to estimate something, and you give your answer to more than one significant figure, you’re doing it wrong!
3. The Hipparcos satellite measured the parallaxes, and hence the distances, to the nearest 120,000 stars. Estimate (remember what we said about estimating above):
(a) The radius of the volume of space centered on the Sun which encompasses the nearest 120,000 stars, and
(b) what the fraction of the stars in our galaxy that is,
using ONLY the following the information:
(1) there are about 70 stars within 5 parsecs of the Sun (see mini-lecture 1.1),
(2) assume the density of stars throughout the galaxy is the same as it is in the region of space local to our Sun,
(3) the Galaxy is approximately a disk about 300 pc in height and 15,000 pc in diameter.
4. Pick any 3 stars from the catalog of stars whose parallaxes were measured by Hipparcos (http://heasarc.gsfc.nasa.gov/db-perl/W3Browse/w3table.pl?tablehead=name=hipparcos&Action=More%20Options ), and calculate their distances. (From the link, scroll down right to the bottom of the page, and click on “Start Search”: this will take you to the catalog. mas stands for milli-arcseconds.)
5. In parsecs, what is the distance to a star with 2 arc seconds of parallax at the Earth? What is the distance to a star with 1/3 arc second of parallax at Earth?
6. Estimate the distances to stars A and B in Diagram 2. The two images are taken 6 months apart. Give the distances in parsecs and in light years.
picture is attached “question-6-picture”.
7. If you wanted to measure parallaxes of stars, would it be better to make the observations from a satellite in the same orbit as Mercury or a satellite in the same orbit as Mars? Why? Illustrate your answer with a diagram.
8. Capella has an apparent magnitude of 0.08. Pollux has an apparent magnitude of 1.14.
a) Which of these two stars has the bigger apparent magnitude number?
b) Which star looks brighter from Earth? How do you know?
c) Castor appears dimmer from Earth than either Pollux or Cappella. Make up a possible apparent magnitude for Castor which is consistent with this observation.
9. Deneb has an apparent magnitude of 1.25 and an absolute magnitude of -7.2. If its distance was doubled, would its apparent magnitude decrease or increase? Would its absolute magnitude decrease or increase?
10. a) The apparent magnitude of a star is -1.0, and its absolute magnitude is 3.0. Is it located closer or further away than 10pc? How do you know?
b) Star A outputs 100 times the energy per second as star B. What is the difference in their absolute magnitudes?