First slide

Gravitational force and laws

Question

If a new planet is discovered rotating around Sun with the orbital radius double that of earth, then what will be its time period (in earth's days)

Moderate

A

1032
B

1023
C

1024
D

1043

Solution

$\begin{array}{l} T^{2} \propto R^{3} \Rightarrow {(\frac{T_{P}}{T_{E}})}^{2} = {(\frac{R_{P}}{R_{E}})}^{3} = {(\frac{2 R_{E}}{R_{E}})}^{3} \\ \Rightarrow \frac{T_{P}}{T_{E}} = (2)^{3 / 2} = 2 \sqrt{2} \\ \Rightarrow T_{P} = 2 \sqrt{2} \times 365 = 1032 .37 = 1032 days \end{array}$

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