Question

The mass of a planet is 3.7 x 1024 kg. If the planet has a radius of 9.2 x 106 m what is the acceleration of gravity for a person on the surface of the planet? Find the escape velocity from the surface of this planet

Answer 1

Step-by-step explanation:

It s given that,

Mass of a planet,
`M=3.7* 10^(24)\ kg`

Radius of a planet,
`R=9.2* 10^(6)\ m`

(1) We need to find the acceleration due to gravity for a person on the surface of the planet. Its formula is given by :

`g=(GM)/(R^2)`

`g=(6.67* 10^(-11)\ Nm^2/kg^2* 3.7* 10^(24)\ kg)/((9.2* 10^(6)\ m)^2)`

`g=2.91\ m/s^2`

(2) The escape velocity is given by :

`v=\sqrt{(2GM)/(R)}`

`v=\sqrt{{(2* 6.67* 10^(-11)\ Nm^2/kg^2* 3.7* 10^(24)\ kg)/(9.2* 10^(6)\ m)}`

v = 7324.61 m/s

Hence, this is the required solution.