## Weight on Earth, Mars and Moon

**Mass and weight are related**: Bodies having large mass also have large weight. A large stone is hard to throw because of its large mass, and hard to lift off the ground because of its large weight. To understand the relationship between mass and weight, consider a freely falling stone, that has an acceleration of magnitude g (g = 9.81 m/s^{2} is the acceleration due to Earth’s gravitational field). Newton’s second law tells us that a force must act to produce this acceleration. If a 1 kilogram stone falls with an acceleration of the required force has magnitude:

*F = ma = 1 [kg] x 9.81 [m/s*^{2}*] = 9.8 [kg m/s*^{2}*] = 9.8 N*

The force that makes the body accelerate downward is its weight. Any body near the surface of the earth that has a mass of 1 kg must have a weight of 9.8 N to give it the acceleration we observe when it is in free fall.

**Example: The weight of a stone on the Earth, on the Mars and on the Moon**

**Weight of a stone on the Earth**

The acceleration due to Earth’s gravitational field is *g** _{Earth}* = 9.81 m/s

^{2}.The weight of a stone with mass

*1 kg*on the Earth can be calculated as:

*F*_{Earth}* = 1 [kg] x 9.81 [m/s*^{2}*] = 9.8 [kg m/s*^{2}*] = 9.8 N*

**Weight of a stone on the Mars**

The acceleration of gravity on the Mars is approximately *38%* of the acceleration of gravity on the earth. The acceleration due to Moon’s gravitational field is *g** _{Mars}* = 3.71 m/s

^{2}.

Therefore the weight of the same stone with mass *1 kg* on the Mars is:

*F*_{Moon}* = 1 [kg] x 3.71 [m/s*^{2}*] = 3.71 [kg m/s*^{2}*] = 3.71 N*

**Weight of a stone on the Moon**

The acceleration of gravity on the Moon is approximately *1/6* of the acceleration of gravity on the earth. The acceleration due to Moon’s gravitational field is *g** _{Moon}* = 1.62 m/s

^{2}.

Therefore the weight of the same stone with mass *1 kg* on the Moon is:

*F*_{Moon}* = 1 [kg] x 1.62 [m/s*^{2}*] = 1.62 [kg m/s*^{2}*] = 1.62 N*

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