Why do the period of revolution increases as the distance from the sun and the planet?
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By Kepler's laws, we know that,
T² is directly proportional to R³.
where T is time period of revolution and and R is distance between sun and earth.
So as the distance increases, the time period increases.
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By, conservation of mechanical energy of a rotating planet around sun,We see that
velocity of the revolving planet = √GM/r
where M is the mass of sun, and r is the radius of orbit of planet around the sun
Now
Time period = 2πr/v = (2π/√GM)*r^3/2
This means 2π/√GM being constant
T is proportional to r^3/2
So, that means,
T^2 is proportional to r^3
This is also what is said by the Kepler's Third Law
Hope this helps you and you've got a satisfying explanation ! ｡◕‿◕｡
velocity of the revolving planet = √GM/r
where M is the mass of sun, and r is the radius of orbit of planet around the sun
Now
Time period = 2πr/v = (2π/√GM)*r^3/2
This means 2π/√GM being constant
T is proportional to r^3/2
So, that means,
T^2 is proportional to r^3
This is also what is said by the Kepler's Third Law
Hope this helps you and you've got a satisfying explanation ! ｡◕‿◕｡
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