How to calculate the gravitational force? Earth Sun

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In another article, we have discussed Gravity and Gravitation, Newton’s universal law of gravitation and the formula for gravitational force. In this article, we are going to learn how to calculate the gravitational force of attraction between two objects like Earth and Sun, Earth and Moon, electron and proton, etc.

Contents of this article:

  1. How to calculate the gravitational force between two objects
  2. Gravitational force between Earth and Sun
  3. The gravitational force between Earth and Moon
  4. Gravitational force between electron and proton

How to calculate the gravitational force between two objects?

One can find the gravitational force of attraction between two objects by using the formula for Newton’s law of gravitational force. If m1 and m2 be the masses of two objects separated by a distance r, then the formula for gravitational force is,

\small {\color{Blue} F=G\frac{m_{1}m_{2}}{r^{2}}}. Where G is the Universal gravitational constant.

To find the gravitational force between two objects we need to use this equation. Obviously, we have to know the values of the masses of two objects and the distance between the objects. And, the value of G in SI unit is 6.67×10-11 N.m2Kg-2 and in CGS unit it is 6.67×10-8 dyn.cm2g-2.

The gravitational force between the Earth and Sun

The mass of Earth is ME = 5.972×1024 kg \small \approx 6×1024 kg

The mass of the Sun or the solar mass is Ms = 1.989×1030 Kg \small \approx 2×1030 Kg

And the average distance between the Sun and the Earth is r= 1.496×1011 m

So, the gravitational force between the Earth and Sun is, \small F= 6.67\times 10^{-11}\times \frac{6\times 10^{24}\times 2\times 10^{30}}{(1.496\times 10^{11})^{2}}.

or, the gravitational force between the Earth and the Sun is, F = 3.576×1022 Newton.

The gravitational force between Earth and Moon

The mass of the Earth is ME = 5.972×1024 kg \small \approx 6×1024 kg

The mass of the Moon is Mm = 7.348×1022 Kg

And the average distance between the Earth and the Moon is, r = 3.844×108 m

So, the gravitational force between the Earth and the Moon is, \small F= 6.67\times 10^{-11}\times \frac{6\times 10^{24}\times 7.348\times 10^{22}}{(3.844\times 10^{8})^{2}}.

or, F = 1.99×1020 Newton.

This is the gravitational force of attraction between the Earth and the Moon.

Gravitational force between electron and proton for the first orbit of a hydrogen atom

The mass of an electron is Me = 9.11×10-31 Kg

and the Mass of a proton is, Mp = 1.673×10-27 kg

The distance between the electron and the proton is equal to the radius of the first Bohr orbit, r = 0.529×10-10 m

So, the gravitational force between the electron and proton is \small F= 6.67\times 10^{-11}\times \frac{9.11\times 10^{-31}\times 1.673\times 10^{-27}}{(0.529\times 10^{-10})^{2}}

or, F = 3.63×10-47 Newton.

This is the gravitational force between a proton and an electron in the first Bohr orbit.

In this article, we learned how to calculate the Gravitational force between two objects separated by a distance. If you have any doubt on this topic you can ask me in the comment section.

Thank you!

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  1. Newton’s universal gravitational law
  2. Contact Forces