a) The acceleration of gravity at the surface of an asteroid is measured as 7.3
ID: 2252480 • Letter: A
Question
a) The acceleration of gravity at the surface of an asteroid is measured as 7.3 x 10^-3 m/s^2. if the asteroid's radius is 10.0 km, what is its density? (assume the asteroid is spherical to sufficient accuracy) b) Jupiter's satellite Ganymede has an almost circular orbit of radius 1.07 x 10^9 m and period of 7.155 d. use these data to find the mass of Jupiter. c) Calculate the orbital period of a satellite just above Earth's atmosphere. (Neglect the difference between the radius of the Earth and the orbital radius of the satellite.)Explanation / Answer
a) a = G M/r^2
M = d* (4/3* pi*r^3)
a = G d 4/3*pi*r
7.3E-3 = 6.67E-11*d*4/3*pi*10.0E3
d=2613 kg/m^3
b) 4 pi^2/T^2 = G M/R^3
4*pi^2/(7.155*24*60*60)^2 = 6.67E-11*M/(1.07E9)^3
M=1.897E27 kg
c) 4*pi^2/T^2 = 6.67E-11*5.97E24/6.37E6^3
T=5062 s
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