A Space-ship Is Launched Into A Circular Orbit Close To The Earth’s Surface. What Additional Velocity Should Now Be Imparted To The Space-ship In The Orbit To Overcome The Gravitational Pull. (Radius Of Earth = 6400 Km And g= 9.8 m/s2)

The masses and radii of the earth and moon are M₁, R₁ and M₂, R₂respectively. Their centres are at distance d apart. What is the minimum speed with which a particle of mass m should be projected from a point midway between the two centres so as to escape to infinity?

Distance between the centres of two stars is 10a. The masses of these stars are M and 16M and their radii a and 2a, respectively. A body of mass m is fired straight from the surface of the larger star towards the smaller star. What should be its minimum initial speed to reach the surface of the smaller star? Obtain the expression in terms of G, M and a.

A mass  (= mass of earth) is to be compressed in a sphere in such a way that the escape velocity from its surface is 3 × 10⁸ m/s (equal to that of light). What should be the radius of the sphere?

A projectile is fired vertically upward from the surface of earth with a velocity Kv_e where v_e is the escape velocity and K < 1. Neglecting air resistance, show that the maximum height to which it will rise measured from the centre of earth is R/(1 – K²) where R is the radius of the earth.

A particle is fired vertically upwards from the surface of earth and reaches a height 6400 km. find the initial velocity of the particle if R = 6400 km andg at the surface of earth is 10 m/s².

Calculate the mass of the sun if the mean radius of the earth’s orbit is 

Imagine a light planet revolving around a very massive star in a circular orbit of radius r with a period of revolution T. On what power of r, will the square of time period depend if the gravitational force of attraction between the planet and the star is proportional to 

Halley’s comet has a period of 76 years and in 1986, had a distance of closest approach to the sun equal to  What is the comet’s farthest distance from the sun if the mass of sun is  units?

Consider on earth satellite so positioned that it appears stationary to an observer on earth and serves the purpose of a fixed relay station for intercontinental transmission of TV and other communications. What would be the height at which the satellite should be positioned and what would be the direction of its motion? Given that the radius of the earth is 6400 km and acceleration due to gravity on the surface of the earth is 9.8m/s².

An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth. (a) Determine the height of the satellite above the earth’s surface. (b) If the satellite is stopped suddenly in its orbit and allowed to fall freely onto the earth. Find the speed with which it hits the surface of the earth. (g = 9.8 ms ^–2 and R_E = 6400 km)