A spaceship is launched into a circular orbit close to the surface of the earth. What additional velocity has now to be imparted to the spaceship in the orbit to overcome the gravitational pull.

Consider two solid uniform spherical object of the same density \(\rho \) . One has a radius R and the other a radius 2R. They are in outer space where the gravitational field from other objects are negligible. If they are at rest with their surfaces touching, then what is the contact force between the objects due to their gravitational attraction?

Choose the correct alternatives.
Acceleration due to gravity increases/decreases with increasing depth(assume the earth to be a sphere of uniform density).

The planet Neptune travels around the sun with a period of 165 yr. Show that the radius of its orbit is approximately thirty times that of the earth's orbit, both being considered as circular.

A particle is fired vertically upwards with a speed of 15 km/s. Find the speed of particle when it goes out of the earth's gravitational pull.

Two steel balls whose masses are 502 kg and 0.25 kg are placed with their centres half a metre apart with what force do they attract each other?

The earth-moon distance is \(3.8\times 10^{ 5 }km\). The mass of the earth is 81 times that of moon. Determine the distance from the earth to the point where the gravitational fields due to the earth and the moon cancel out.

A rocket is fired from the earth towards the sun. At what distance from the earth's centre is the gravitational force on the rocket zero? Mass of the sun = 2 x 10³⁰ kg, mass of the earth = 6 x 10²⁴ kg. Neglect the effect of other planets etc. (orbital radius = 1.5 x 10¹¹ m).

A star 2.5 times the mass of the sun and collapsed to a size of 12 km rotates with a speed of 1.2 rev. per second. (Extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity? (mass of the sun = 2 x 10³⁰ kg).

State Kepler's laws of planetary motion.
What would be the speed of rotation of the earth in order that a body on the equator has no weight?
Determine the apparent weights of the bodies situated at a latitude of 60° and at the poles. The radius of the earth = 6400 km and g = 9.8 ms^-1.