Question

A satellite originally moves in a circular orbit of radius R around the Earth. Suppose it is moved into a circular orbit of radius 4R. What happens to the satellite's speed?

Answer 1

Answer:

The speed of satellite moving into circular orbit of radius 4R will become half of the speed of satellite moving into circular orbit of radius R.

Explanation:

Speed of satellite revolving around the central body in a circular path:

$v=\sqrt{\frac{G\times M}{R}}$

Where :

G = gravitational constant = $6.673 \times 10^{-11} Nm^2/kg^2]$

M = Mass of body around which satellite is orbiting

R = radius of the orbit from the satellite

A satellite originally moves in a circular orbit of radius R around the Earth.The velocity of satellite will be ;

$v=\sqrt{\frac{G\times M}{R}}$..[1]

If the same satellite moves in a circular orbit of radius $R around the Earth.The speed of satellite will be :

$v'=\sqrt{\frac{G\times M}{4R}}$..[2]

Dividing [1] and [2]:

$\frac{v}{v'}=\frac{\sqrt{\frac{G\times M}{R}}}{\sqrt{\frac{G\times M}{4R}}}$

$\frac{v}{v'}=2$

$v'=\frac{1}{2}v$

The speed of satellite moving into circular orbit of radius 4R will become half of the speed of satellite moving into circular orbit of radius R.

Answer 2

 satellite originally moves in a circular orbit of radius R around the Earth. Suppose it is moved into a circular orbit of radius 4R.

(i) What does the force exerted on the satellite then become?

eight times largerfour times larger   one-half as largeone-eighth as largeone-sixteenth as large(ii) What happens to the satellite's speed?eight times largerfour times larger   one-half as largeone-eighth as largeone-sixteenth as large(iii) What happens to its period?eight times largerfour times larger   one-half as largeone-eighth as largeone-sixteenth as large