Let the period of revolution of s planet at a diatance R from a star be T . prive that if it was at a dustsnce if2R from the star ,its period of revolution will be √8T
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according to Kepler's third law , the square of orbital period of revolution T of a planet around a star is directly proportional to the cube of the mean distance R of the planet from the star.
T^2inversly R^3
T^2 =K(R)^3......(1)
where ,K is constant of proportionality.
2. when the planet is at a distance of 2R revolution T' will be
T'^2= (2R)^3
T^2= K (2R)^3.....(2)
3. dividing equation (1)& (2),we get,
T^2/T,^2= (R)^2/ (2R)^3
T^2/T'^2=1/8
T' =8√T
Thus, for a planet at a distance of 2R from the star ,it's period of revolution will be 8√T
T^2inversly R^3
T^2 =K(R)^3......(1)
where ,K is constant of proportionality.
2. when the planet is at a distance of 2R revolution T' will be
T'^2= (2R)^3
T^2= K (2R)^3.....(2)
3. dividing equation (1)& (2),we get,
T^2/T,^2= (R)^2/ (2R)^3
T^2/T'^2=1/8
T' =8√T
Thus, for a planet at a distance of 2R from the star ,it's period of revolution will be 8√T
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