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 km.
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)
3. Consider the mechanical energy of a body at rest on the ground at the Earth's equator, at re=6400 km
Consider the mechanical energy of the same body at rest on the ground at the South pole, at re=6400 km. For this problem, we consider the Earth to be spherical.
(Remember, the object at the equator traces a circular path, the object at the Pole does not.)
G=6.67×10^−11 Nm^2 kg^−2, and the mass of the Earth is M = 5.97×10^24 kg
1) escape speed = sqrt(2GM/R)
where G = gravitational constant
M = mass , R = radius
V(esc) = sqrt(2*6.67*10^-11*9.4*10^20 / 476000^2)
= 0.55 m/s
so the escape speed is 0.55 m/s
1. Ceres is the largest asteroid. Its mean radius is 476 km and its mass is...
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