A spacecraft consumes more fuel in going from earth to the moon than it takes for a return trip. Comment on this statement.

A mass of 6 × 10²⁴ Kg (equal to the mass of the earth) is to be compressed in a sphere in such a way that the escape velocity from its surface is 3 × 10⁸ ms^-1. What should be the radius of the sphere?

A particle is fired vertically upward with a speed of 15 km s^-1. With what speed will it move in interstellar space. Assume only earth’s gravitational field.

A satellite is in an elliptic orbit around the earth with aphelion of 6R and perihelion of 2 R where R = 6400 km is the radius of the earth. Find eccentricity of the orbit. Find the velocity of the satellite at apogee and perigee. What should be done if this satellite has to be transferred to a circular orbit of radius 6R?

[G = 6.67 × 10 ^{- 11} SI units and M = 6 × 10²⁴ kg]

A satellite is to be placed in equatorial geostationary orbit around earth for communication.

(a) Calculate height of such a satellite.

(b) Find out the minimum number of satellites that are needed to cover entire earth so that at least one satellites is visible from any point on the equator.

[M = 6 × 10²⁴ kg, R = 6400 km, T = 24h, G = 6.67 × 10 ^{- 11} SI units]

Which of the following are true?

Two satellites A and B move round the earth in the same orbit. The mass of B is twice the mass of A.

A particle is kept at rest at a distance R (earth’s radius) above the earth’s surface. The minimum speed with which it should be protected so that it does not return is

A rocket is fired vertically with a speed of 5 km s^-1 from the earth’s surface. How far from the earth does the rocket go before returning to the earth? Mass of the earth = 6.0 × 10²⁴ kg; mean radius of the earth = 6.4 × 10⁶ m; G = 6.67 × 10^–11 N m2 kg^–2.

Give one example each of central force and non - central force.

The time period of an earth-satellite in circular orbit is independent of