Fall 2000 ASTR 1120-001 General Astronomy Problem Set 3 Fall 2000 ASTR 1120-001 General Astronomy: Stars & Galaxies.
Problem Set 3. Due T 17 Oct

1. Parallax

As of today (24 Sep 2000) there are 58 confirmed planets or brown dwarfs known around main sequence stars other than the Sun. The latest data can be found in the Extra-solar Planets Catalog.

To date the nearest star with a planet is e Eridani (HD 22049), the 6th nearest star system beyond the Sun and the a Cen triple system. e Eri is 0.8 times the mass of the Sun, and the planet is 1.2-4.7 times the mass of Jupiter, with a 6.9 year period. The Hipparcos satellite measured a parallax ( http://astro.estec.esa.nl/Hipparcos/table361.html) of 0.31075 ± 0.00085 arcseconds (the ± number is the uncertainty in the measured parallax). What is the distance to e Eri? For 1 point extra credit, figure out also the uncertainty in the distance, and write your answer as x ± y parsecs.

e Eri is ______________________ parsecs away from us.

2. Inverse Square Law

h+c Persei is a pretty double open cluster of stars which can be seen with binoculars in the northern sky. A main sequence A star (just like Vega or Sirius) appears in h+c Persei to be 15 magnitudes (= a factor of 106) fainter than Sirius. The distance to Sirius is known from its parallax to be 2.63 parsecs away. How far away is h+c Persei, in parsecs? [Hint: use the inverse square law of distances. You can assume that Sirius and the A star have the same luminosity.]

h+c Persei is ______________________ parsecs away from us.

3. Main Sequence Fitting

The Pleiades cluster is ______________________ parsecs away.

4. HR Diagram

Below is the beginnings of an HR diagram. Complete the labeling of the axes (Which is surface temperature? Which is spectral type? Which is luminosity? Which is absolute magnitude? What are the units in each case?). Here is a list of stars with their spectral types and absolute magnitudes. The number on each spectral type is the subtype within the spectral type. The subtypes run from 0 to 9, with 0 being hottest, 9 being coolest.

 Star Spectral Type Absolute Magnitude A Sun G2 5.0 B Rigel Kent (a Cen A) G2 4.34 C a Cen B K4 5.70 D Proxima Cen (a Cen C) M5 15.45 E Barnard's Star M5 13.24 F Sirius A (a CMa) A1 1.45 G Sirius B A5 11.5 H Betelgeuse (a Ori) M2 -5.14 I Rigel (b Ori) B8 -6.69 J Arcturus (a Boö) K1 -0.31 K Capella (a Aur) G8 -0.48 L Vega (a Lyr) A0 0.58 M b Cen B1 -5.42 N Procyon A (a CMi) F5 2.68 O Procyon B F 13.1 P Kapteyn's star M0 10.89 Q Deneb (a Cyg) A2 -8.73 R e Eri K2 3.73

Plot the stars on the HR diagram. I already plotted star A as an example. Indicate on the diagram which stars are on the main sequence, which stars are red giants, which stars are supergiants, and which stars are white dwarfs.

5. Stefan-Boltzmann Law

Sirius, the brightest star in the sky bar the Sun, is actually a binary system. Sirius B is 10 magnitudes (factor of 104) fainter than Sirius A, but Sirius B's surface temperature is about twice that of Sirius A. What is Sirius B's radius relative to that of Sirius A?