Question

A satellite is revolving in a circular orbit at a height 'h' above the surface of the earth of radius 'R'. The speed of the satellite in its orbit is one-fourth the escape velocity from the surface of the earth. The relation between 'h' and 'R' is ______.

Options

• h = 2R

• h = 3R

• h = 5R

• h = 7R

Answer 1

A satellite is revolving in a circular orbit at a height 'h' above the surface of the earth of radius 'R'. The speed of the satellite in its orbit is one-fourth the escape velocity from the surface of the earth. The relation between 'h' and 'R' is h = 7R.

Explanation:

According to question, speed of satellite in its orbit.

v_c = `1/4"v"_"e"`

(v_e = escape speed)

`sqrt("GM"/("R"+"h")) = 1/4 sqrt((2"GM")/("R"))` ;

`sqrt("GM"/("R"+"h"))=1/16xx(2"Gm")/("R")`

R + h = 8(R)

R + h = 8R

7R = h