## Question

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:

### Solution

The gravitational force of attraction exerted by the earth on the satellite is the necessary centripetal force. Therefore, if *h* be the height of the satellite above the earth’s surface, then

Where m is the mass of the satellite, (*R _{e}* +

*h*) is the distance of the satellite from the centre of the earth and

*v*is the orbital velocity of the satellite. If the period of revolution of the satellite be

_{0}*T*. then

Substituting from this the value of *v _{0}* in eq. (i), we get

Here, orbital radius and period of revolution *T* = 98 × 60 = 5.88 × 10^{3} *s*.

#### SIMILAR QUESTIONS

At a point above the surface of the earth, the gravitational potential is and the acceleration due to gravity is 6.4 ms^{–2}. Assuming the mean radius of the earth to be 6400 km, calculate the height of this point above the earth’s surface. ^{ }

The mass of the earth is and its radius is m. How much work will be done in taking a 10-kg body from the surface of the earth to infinity? What will be the gravitational potential energy of the body on the earth’s surface? If this body falls from infinity to the earth, what will be its velocity when striking the earth?

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

Calculate the velocity of projection of a particle so that the maximum height attained by the particle is 0.5 *R _{e}*, where

*R*is radius of earth. The mass of earth is

_{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.

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.