1. Ceres is the largest asteroid. Its mean radius is 476 km and its mass is 9.4×10^20 kg. Using this, and G = 6.67×10^−11 Nm^2 kg^−2, and approximating it as a sphere, compute the speed required to escape the gravity on the surface of Ceres.
Speed = ___ m.s^−1. (to two significant figures, don't use scientific notation)
2. Consider the mechanical energy of a body in geostationary orbit above the Earth's equator, at rGS = 42000.
Consider the mechanical energy of the same body on Earth at the South pole, at re = 6400 km. For this problem, we consider the Earth to be spherical. (Remember, the object at the equator is in orbit, the object at the Pole is not in orbit.)
G = 6.67×10^−11 Nm^2 kg^−2, and the mass of the Earth is M = 5.97×10^24 kg.
What is the difference in the mechanical energy per kilogram between the two?
E= ___ MJ.kg^−1 (to two significant figures, don't use scientific notation).
1
Expert's answer
2020-03-23T10:56:03-0400
1) Now, applying conservation of energy,
rGMm=2mv2
v=r2GM=4670002(6.67⋅10−11)(9.4⋅1020)=520sm
2) Mechanical energy per kilogram at the surface of the earth
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