Question

If Earth has a mass of 5.972 × 10^24 kg and Mars has a mass of 6.39 × 10^23 kg, and the distance between them is 225 x 10^6 m, with what force does Earth pull on Mars?

Answer 1

`5.03xx10^21` Newtons

Explanation:

Newton's law of gravitation states that force of gravity `F` between two objects of mass `m_1` and `m_2` at a distance of `r` from each other is given by

`F=G(m_1m_2)/r^2`, where `G` is gravitational constant whose value is `6.67xx10^(-11)` `Nm^2/(kg.^2)`

Here the objects are Mars, whose mass is `6.39xx10^23` kg. and Earth with mass `5.972xx10^24` kg. As the distance between two is `225 x 10^6m`.

Then Earth pulls Mars with a force `F`, where

`F=6.67xx10^(-11)(6.39xx10^23xx5.972xx10^24)/(225xx 10^6)^2`,

= `(6.67xx6.39xx5.927)/225^2xx10^((-11+23+24-12))`

= `0.00503xx10^24`

= `5.03xx10^21` Newtons

The number appears to be very large, but just divide it by the mass of Mars to get the accelaration caused on Mars by Earth's pull i.e.

`(5.03xx10^21)/(6.39xx10^23)=0.787xx10^(-2)=7.87xx10^(-3)` `m/(sec^2)`

which is a very small number as compared to accelaration due to gravity `9.8` `m/(sec^2)`.