Gravitation — Practice

Question 1

Find g at a height equal to R above Earth's surface.

Accepted Answer

Distance from centre = 2R. g' = GM/(2R)^2 = g/4 = 2.45 m/s^2.

Question 2

Find the orbital velocity of a satellite at 300 km height (R = 6400 km, M = 6e24 kg).

Accepted Answer

r = 6700 km = 6.7e6 m. v_o = sqrt(GM/r) = sqrt(6.67e-11 x 6e24 / 6.7e6) = sqrt(5.97e7) = 7.73 km/s.

Question 3

Calculate the escape velocity on the Moon (g = 1.62 m/s^2, R = 1740 km).

Accepted Answer

v_esc = sqrt(2gR) = sqrt(2 x 1.62 x 1.74e6) = sqrt(5.64e6) = 2.37 km/s.

Question 4

If Earth's period is 1 year at radius R, find the period of a planet at radius 4R.

Accepted Answer

Kepler's third law: T^2 proportional to a^3. (T/T_E)^2 = (4R/R)^3 = 64, so T = 8 years.

Question 5

Why is g zero at the centre of the Earth?

Accepted Answer

At the centre, Earth's mass surrounds the point symmetrically in all directions, so the gravitational forces cancel and the net force (hence g) is zero.

Practice — Gravitation

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