The moon takes about 27.3 days to revolve round the earth in a nearly circular orbit of radius 3.84 × 10⁵ Km. Calculate the mass of the earth from these data.

A pendulum having a bob of mass m is happening in a ship sailing along the equator from east to west. When the ship is stationary with respect to water the tension in the string is T_0.

(a) Find the speed of the ship due to rotation of the earth about its axis.

(b) Find the difference between T₀ and the earth’s attraction on the bob.

(c) If the ship sails at speed . what is the tension in the string? Angular speed of earth’s rotation is ω and radius of the earth is R.

The time taken by the Mars to revolve round the sun is 1.88 years. Find the ratio of average distance between Mars and the sun to that between the earth and the sun.

A Mars satellite moving in an orbit of radius 9.4 × 10³ Km takes 27540 s to complete one revolution. Calculate the mass of Mars.

A satellite of mass 1000 kg is supposed to orbit the earth at a height of 2000 Km above the earth’s surface. Find

(a) Its speed in the orbit.

(b) Its kinetic energy.

(c) The potential energy of the earth-satellite system and

(d) Its time period. Mass of the earth = 6 × 10²⁴ Kg.