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

Correct option is

 

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, (Re + h) is the distance of the satellite from the centre of the earth and v0 is the orbital velocity of the satellite. If the period of revolution of the satellite be T. then

                              

Substituting from this the value of v0 in eq. (i), we get

                             

                              

Here, orbital radius  and period of revolution T = 98 × 60 = 5.88 × 103 s.  

SIMILAR QUESTIONS

Q1

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.   

Q2

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? 

Q3

 

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?

Q4

A body of mass m is moved from the surface of the earth to a height (his not negligible in comparison to radius of earth Re). Prove that the increase in potential energy is  

Q5

Calculate the velocity of projection of a particle so that the maximum height attained by the particle is 0.5 Re, where Re is radius of earth. The mass of earth is Me.

Q6

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 =  Nmkg–2 

Q7

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.

Q8

 

(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?

Q9

 

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.

Q10

 

If the period of revolution of an artificial satellite just above the earth be Tand the density of earth be then prove that ρT2 is a universal constant. Also calculate the value of this constant.