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?

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Tringa0 Tringa0 · Answer 2 · 2020-01-22T11:00:10+01:00

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:

[tex]v=\sqrt{\frac{G\times M}{R}}[/tex]

Where :

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

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 ;

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

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

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

Dividing [1] and [2]:

[tex]\frac{v}{v'}=\frac{\sqrt{\frac{G\times M}{R}}}{\sqrt{\frac{G\times M}{4R}}}[/tex]

[tex]\frac{v}{v'}=2[/tex]

[tex]v'=\frac{1}{2}v[/tex]

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.