Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB. These planets are revolving in the circular orbits or radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits?

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Physics Class 12th Physics NCERT Exemplar Solutions Class 12th Chapter Eight Gravitation

Two planets A and B of equal mass are having their period of revolutions T_A and T_B such that T_A = 2T_B. These planets are revolving in the circular orbits or radii r_A and r_B respectively. Which out of the following would be the correct relationship of their orbits?

Option 1 -

$2 r_{A}^{2} = r_{B}^{3}$

Option 2 -

$r_{A}^{3} = 2 r_{B}^{3}$

Option 3 -

$r_{A}^{3} = 4 r_{B}^{3}$

Option 4 -

$T_{A}^{2} - T_{B}^{2} = \frac{π^{2}}{G M} (r_{B}^{3} - 4 r_{A}^{3})$

2 Views | Posted 3 months ago

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1 Answer

Answered by

Payal Gupta | Contributor-Level 10

3 months ago

Correct Option - 3

Detailed Solution:

According to kepler’s third law of time period –

${(\frac{T_{A}}{T_{B}})}^{2} = {(\frac{r_{A}}{r_{B}})}^{3} \Rightarrow \frac{r_{A}}{r_{B}} = 4^{1 / 3}$

$\Rightarrow r_{4}^{3} = 4$ $r$ $B$ $3$

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