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ASTR 1403 Homework Set 5 Due 11/14/23 The Earth’s orbit has a semi-major axis of a = 1.00 AU and an orbital period of P =1 sidereal year = 365.256 days = 3.156 x 10°7 s. Compute the orbital periods of bodies orbiting the Sun with each of the following semi-major axes. a) a=0.1AU b) a=10AU c) a=100AU d) a=1000AU e) a=10,000AU 1AU=1.496 x 10"8 km = 1.496 x 10M1 m = 1.496 x 10M3 cm. GM(sun) = 1.327 x 1020 m"3/s"2 = (Newton’s Constant) x (Mass of Sun) Note - You will need Kepler’s Third Law (K3L). You may use either the Keplerian form or the Newtonian form of K3L. Both are valid and both will do the trick. The planet Neptune has a large moon, Triton. Triton orbits at a distance from Neptune of a = 354,800 km. The orbital period of Triton is P = 5.88 days = 508,000 s. What is the mass of Neptune? Newton'’s constant is G = 6.673 x 10/(-11) m"3/kg s"2. A spacecraft orbits Venus at an altitude of h = 250 km above the surface of Venus. The radius of Venus is R = 6050 km. The orbit of the spacecraft is circular. a) What do you use for the semi-major axis a of the spacecraft’s orbit? b) What is the orbital period P of the spacecraft? c) What is the orbital speed of the spacecraft? The mass of Venus is M(Venus) = 4.87 x 10724 kg. Newton’s constant is G = 6.673 x 104(-11) m"3/kg s"2.

The planet Mars has a semi-major axis of a = 1.52 AU = 2.274 x 1078 km and an eccentricity of e = 0.093. The albedo of Mars is A= 0.25. the radius of Mars is R = 3,390 km. The luminosity of the sunis L _sun = 3.83 x 10/(33) erg/s. 4., Assume that Mars is a distance of 1.52 AU = 2.274 x 1078 km from the sun. a) Compute the flux from the sun at Mars. b) Compute the rate of energy absorption by Mars. C) Compute the temperature of Mars. 5. The Mars-Sun distance at perihelionisr_p = a(1 - e) and the Mars-Sun distance at aphelionisr_a = a(1 +e). The eccentricity of Mars is e = 0.093. The albedo of Mars isA=0.25. a) Compute the Mars-Sun distance at perihelion and the flux from the sun at Mars at perihelion. b) Compute the temperature of Mars at perihelion. C) Compute the Mars-Sun distance at aphelion and the flux from the sun at Mars at aphelion. d) Compute the temperature of Mars at aphelion.