Question

mass of the planet is 12 times that of earth and its radius is thrice that of earth , then find the escape velocity on that planet ?? ​

Answer 1

The escape velocity on the planet is approximately 178.976 km/s

Step-by-step explanation:

The escape velocity for Earth is therefore given as follows

The formula for escape velocity,
`v_e`, for the planet is
`v_e = \sqrt{(2 \cdot G \cdot m)/(r) }`

Where;

`v_e` = The escape velocity on the planet

G = The universal gravitational constant = 6.67430 × 10⁻¹¹ N·m²/kg²

m = The mass of the planet = 12 × The mass of Earth,
`M_E`

r = The radius of the planet = 3 × The radius of Earth,
`R_E`

The escape velocity for Earth,
`v_e_E`, is therefore given as follows;

`v_e_E = \sqrt{(2 \cdot G \cdot M_E)/(R_E) }`

`\therefore v_e = \sqrt{(2 * G * 12 * M)/(3 * R) } = \sqrt{(2 * G * 4 * M)/(R) } = 16 * \sqrt{(2 * G * M)/(R) } = 16 * v_e_E`

`v_e` = 16 ×
`v_e_E`

Given that the escape velocity for Earth,
`v_e_E` ≈ 11,186 m/s, we have;

The escape velocity on the planet =
`v_e` ≈ 16 × 11,186 ≈ 178976 m/s ≈ 178.976 km/s.