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## Physics Tutorials

### Gravity and Satellites

Gravity, a force that pulls masses together, is described by Newton’s Law of Universal Gravitation: two bodies attract each other with a gravitational force which is proportional to the mass of each body and inversely proportional to the square of the distance between their centers.

The motion of satellites is controlled by gravity.

#### Explanation

This means that the greater the mass of the objects the greater the force of gravity between them. The force of gravity between these two objects also decreases with distance.  Near the Earth’s surface the force of gravity can be found with the formula F=mg where (F) is the force, (m) is the mass, and (g) is the acceleration of 9.8 m/s/s.  Newton’s Law of Universal Gravitation extends beyond the earth.  The force of gravity can be found with the formula F=(G m1m2)/d2 where F is the force, G is the gravitational constant G = 6.67 x 10-11 Nm2/kg2, m1 is the mass of one body, m2 is the mass of the other body, and d is the distance between the centers of the two bodies in meters. Satellites orbiting the earth have velocity.  They are held in an orbit by the force of gravity between the earth and the satellites.  This is similar to an apple falling from a tree.  When an apple falls it hits the ground.  A satellite is constantly falling toward the ground, it just never reaches the ground like an apple would.  This is because the earth curves out from under the satellite so it never reaches the earth’s surface.

#### Question

A satellite has a mass of 1000 kg and is orbiting the earth which has a mass of 5.9742 x1024 kg.  If the satellite and the earth are centered 500 km apart, then what is the force of gravity between the satellite and the earth?