What is the acceleration due to gravity at the surface of Titania?
Titania, the largest moon of Uranus, has a radius that is approximately 1/8 that of Earth and a mass about 1/1700 that of Earth. What is the acceleration due to gravity at the surface of Titania? Additionally, could you provide information on the average density of Titania? It is noted that this density is less than that of rock, which suggests that Titania is primarily composed of ice. Thank you for your assistance!
4 Answers
Jan 28, 2025
g' = g(m/M)(R/r)^2; where g = 9.81 m/s^2, m = M/1700, r = R/8. Thus...
g' = 9.81(1/1700)(8)^2 = 0.369 m/s^2 on Titania. ANS.
rho = m/(4/3 pi r^3) = (M/1700)/(4/3 pi (R/8)^3) = ? the density kg/m^3 of Titania R = 6400E3 m Earth radius and look up M = ? Earth's mass in kg. ANS.
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