Question

# 1. Ceres is the largest asteroid. Its mean radius is 476 km and its mass is...

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)

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

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