Question

a satellite orbiting around Earth of radius R is shifted to an Orbit of radius 2 hour how many times the time taken for one Revolution increased ?

Answer 1

1×120min/2pie R solve kr lena bhai

Answer 2

Given:

Initial orbital radius R

Final orbital radius 2 R

To Find:

Increase in the period of orbit. T'=?

Calculation:

Orbital velocity (for radius R) is given by:

$v=\sqrt{\frac{GM}{R}}$

Orbital velocity (for radius 2R) is given by:

$v'=\sqrt{\frac{GM}{2R}}$

If T is the orbital period for radius R and T' is the orbital period for radius 2 R, then

$\frac{T'}{T}=\frac{2\pi (2R)/v'}{2\pi R/v}\\\frac{T'}{T}=\frac{2v}{v'}=\frac{2\sqrt{GM/R}}{\sqrt{GM/2R}}\\\frac{T'}{T}=2\sqrt 2$

The period increased by $2\sqrt 2$ times.

Learn more about: orbital period and radius

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