The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0 × 10³ km. Find the mass of Mars.
{Given 4π²/G = 6 × 10¹¹ N⁻²kg²}
The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0 × 10³ km. Find the mass of Mars.
{Given 4π²/G = 6 × 10¹¹ N⁻²kg²}
Option 1 -
3.25 * 10²¹ kg
Option 2 -
6.00 * 10²³ kg
Option 3 -
5.96 * 10¹⁹ kg
Option 4 -
7.02 * 10²⁵ kg
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1 Answer
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Correct Option - 3
Detailed Solution:T² = (4π²r³)/GM
⇒ M = (4π²r³)/ (G T²)
⇒ M = 6 × 10¹¹ × (9 × 10? )³ / (450 × 60)²
= 6.48 x 10²³ kg
(Note: There is a calculation error in the source image. Using the formula and given values: M = (6e11 * (9e6)^3) / (27000)^2 = 6e23 kg)
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= 107 m
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