Astr1010, Homework #1

due at the beginning of class, Monday Sept. 15

SHOW ALL WORK!!!

Parralax; p = 1/r p = parallax in arcsec, r = distance in pc

Kepler's 3rd Law; P² = a³ P = period in years, a = semimajor axis in AU

v_esc = G = gravitational constant, M = mass of planet, r = radius of

planet

F_G = Gm₁m₂/r² m₁ & m₂ are masses of interacting bodies

r = distance separating them

1. The closest star to us, Proxima Centauri, is 1.3 pc away. What would be the parallax of this star?

2. What is the period of a comet whose orbital semi-major axis is 30 AU?

3. How much stronger or weaker is the Sun's gravitational force on Venus as opposed to Earth? Venus data: mass = 0.82 Earth masses, a = 0.72 AU.

4. Calculate the escape velocity of Earth, give your answer in meters/sec. How many times greater or smaller is the escape velocity of a planet which has 8 times the mass of the Earth and 2 times the radius of the Earth?