Question

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. How much more mechanical energy per kilogram does an object on the ground at the Equator than on the ground at the Pole?
2. E= ___ MJ.kg^−1 . (2 sig figs, do not use scientific notation)

Answer 1

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