## Question

A space-craft is launched in a circular orbit near the earth. How much more velocity will be given to the space-craft so that it will go beyond the attraction force of the earth. (Radius of the earth = 6400 km, *g* = 9.8 m/s^{2}).

### Solution

The velocity of space-craft in a circular orbit close to the earth’s surface is given by

and the escape velocity is given by

The additional velocity required by the space-craft to go beyond earth’s gravitational attraction, that is, to escape is

#### SIMILAR QUESTIONS

The radius of earth is 6400 km and mass is kg. What will be the gravitational potential energy of a body of 200 kg placed at a height of 600 km from the surface of the earth?

.

A body of mass *m* is moved from the surface of the earth to a height *h *(*h*is not negligible in comparison to radius of earth *R _{e}*). Prove that the increase in potential energy is

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_{e}*M*.

_{e}
A satellite is revolving in a circular orbit at a distance of 2620 km from the surface of the earth. Calculate the orbital velocity and the period of revolution of the satellite. Radius of the earth = 6380 km, mass of the earth = Nm^{2 }kg^{–2}. ^{ }

A satellite is revolving in a circular orbit at a distance of 3400 km. calculate the orbital velocity and the period of revolution of the satellite. Radius of the earth = 6400 km and *g* = 9.8 ms^{ –2}.

(i) A satellite is revolving in an orbit close to the earth’s surface. Taking the radius of the earth as find the value of the orbital speed and the period of revolution of the satellite.

(ii) What is the relationship of this orbital speed to the velocity required to send a body from the earth’s surface into space, never to return?

An artificial satellite revolving coplanar with the equator around the earth, appears stationary to an observer on the earth. Calculate the height of the satellite above the earth.

An artificial satellite is revolving at a height of 500 km above the earth’s surface in a circular orbit, completing one revolution in 98 minutes. Calculate the mass of the earth. Given:

If the period of revolution of an artificial satellite just above the earth be *T*and the density of earth be then prove that ρT^{2} is a universal constant. Also calculate the value of this constant.

An artificial satellite of mass 200 kg revolves around the earth in an orbit of average radius 6670 km. Calculate its orbital kinetic energy, the gravitational potential energy and the total energy in the orbital.

(Mass of earth = 6.0 × 10^{24} kg, *G* = 6.67 × 10^{–11} Nm^{2} kg^{ –2}).