Weight

Weight is the gravitational force that the Earth exerts on bodies that are close to its surface.

Suppose a body of mass m is close to the surface of the Earth and that we want to calculate the gravitational force exerted on it by the Earth:

In this situation, the mass m1 is the mass of the Earth MT, m2 is the mass of the body m and r is the distance between the latter and the center of the Earth.

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If the radius of the earth is much larger than the distance between the body and the surface of the Earth, we can make the following approximation:

the magnitude of the gravitational force will be:

Substituting in the preceding equation the values of G, MT and RT we obtain:

This constant is called the acceleration of gravity.

By substituting it in the expression of the gravitational force we obtain:

As the weight points vertically towards the center of the Earth, we can write it in the vectorial form:

In the following table you will find the gravitational acceleration values for the different planets of the solar system. They were calculated using the law of universal gravitation. Your weight would be different if you were on the surface of another planet.

Planet Masses
(x 1023 kg)
Radius
(x 103 m)
g (m/s2)
Mercury 3.3 2439 3.70
Venus 48.68 6051 8.87
Earth 59.74 6371 9.82
Mars 6.418 3396 3.71
Jupiter 18986 69911 25.92
Saturn 5684.6 60268 10.44
Uranus 868.1 25559 8.86
Neptune 1024.3 24764 11.14
Solar System. Source: NASA.

Here you can find Newton’s laws problems.

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