Question

The time period of earth taken as T and its distance from sun R.what will be the distance of a certain planet from sun whose time period is 64 times that of earth ?

Answer 1

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Answer 2

The distance from certain planet from sun is 16R

Given:

Time period = T  

Distance from sun to earth = R  

Solution:

So, according of the Kepler’s law of planetary motion, we have,

$T^{2} \propto R^{3}$

So, the equation for earth is given as:

$T_{E}^{2} \propto R_{E}^{3}$

The equation for certain planet is given as:

$T_{P}^{2} \propto R_{P}^{3}$

On dividing both the equations, we get,

$\frac{T_{E}^{2}}{T_{P}^{2}}=\frac{R_{E}^{3}}{R_{P}^{3}}$

On substituting the values from question, we get,

$\frac{T^{2}}{(64 T)^{2}}=\frac{R^{3}}{R_{P}^{3}}$

$\frac{1}{64^{2}}=\frac{R^{3}}{R_{P}^{3}}$

$R_{P}^{3}=4096 R^{3}$

On taking cube root on both sides, we get,

$R_{P}=16 R$