The moon's mass is less than Earth's, which is why astronauts weigh less on its surface.
Gravity is the attractive force between two bodies. It is what keeps the moon orbiting around the Earth and what keeps our feet planted on the ground. The force of gravity can be stronger or weaker depending upon two factors, mass and distance.
Mass
Mass is the first factor that determines the gravitational force. There are two masses to consider when determining the amount of gravity. The more mass each has, the greater the pull between them. For example, the mass of the Earth is greater than that of the Moon. This means that a person, whose mass is the same on both the Earth and Moon, will experience a larger gravitational force on Earth than on the Moon since the Earth has more mass. Jupiter has a greater mass than Earth, making the gravitational force exerted on Jupiter much more than that of Earth.
Distance
The distance between the two objects plays a large role in determining the amount of gravitational force between them. The further the objects are apart the less gravitational attraction they have to each other. The further away, for instance, the planets are from each other, the less attraction there is between them. However, it also applies in other circumstances. For example, you will feel a greater gravitational force standing on the surface of Earth than if you were flying in a hot air balloon, albeit the difference is small. This is because the hot air balloon is a greater distance from the center of mass of the Earth.
Formula
The formula of gravitational force is the product of the masses multiplied by the gravitational constant divided by the square of their distance, or F=G (m1 x m2) / r^2. F stands for the gravitational force. G is for the gravitational constant. M1 is the mass of object one. M2 is the mass of the second object. R is the distance between the two bodies. The gravitational constant, G, is 6.67 x 10^-11 Nm^2/kg^2.
Proportionality
The gravitational force experienced differs proportionally between the two factors. The mass of either object is directly proportional to the amount of gravitational force. For example, if the mass of object one is doubled, the amount of gravitational force also doubles. The force between the objects is inversely proportional to the square of the distance. This means that if the distance between the two objects were to double, the gravitational force between the objects would be only be a quarter as strong as it was at the original distance.
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