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final-practice

# final-practice - Instructions Before you do anything else...

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Angular vs. actual size (small-angle formula): D = α d 206265 arcsec Kepler’s Third Law, with M in Solar masses, a in AU, and P in years: P 2 = a 3 M Kepler’s Third Law, with M in Earth masses, a in km, and P in seconds: P 2 = 10 - 4 × a 3 M Newton’s Second Law of Motion: F = ma Newton’s Law of Gravity: F = G m 1 m 2 r 2 Wien’s Law: λ peak = 0 . 0029 m K T Stefan-Boltzmann Law: F = σ T 4 σ = 5 . 67 × 10 - 8 W m - 2 K - 4 Temperatures: T F = 9 5 T C + 32 T C = 5 9 ( T F - 32) T K = T C + 273 Doppler e ff ect: Δ λ λ 0 = v c Volume of a sphere of radius R : V = 4 3 π R 3 Density: density = mass volume Typical speed of molecules of mass m in a gas at temperature T : v gas = 3 kT m k = 1 . 38 × 10 - 23 kg m 2 s - 2 K - 1 Escape speed for planet of mass M and radius R : v esc = 2 GM R Center of mass: r 1 M 1 = r 2 M 2 2
1. The Roche zone is the region a) where graviational resonances clear a gap in the ring sys- tem. b) around a planet in which a moon is torn apart by tidal forces. c) of a giant planet where strong counter-rotating winds are seen. d) between Mars and Jupiter where many asteroids are found. e) around a planet in which large moons are found.

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