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Physics Tutorial: Gravity and Satellites

Gravity, a force that pulls masses together, is described by Newton’s Law of Universal Gravitation:

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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.
 
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.
 

 


The motion of satellites is controlled by gravity.

 

 

 

 


 

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.

 

Gravity's ARC: The Story of Gravity from Aristotle to Einstein and Beyond

Gravity's ARC: The Story of Gravity from Aristotle to Einstein and Beyond

In Gravity's Arc, you'll discover how some of the most colorful, eccentric, and brilliant people in history first locked, then unlocked the door to understanding one of nature's most essential forces. You'll find out why Aristotle's misguided conclusions about gravity became an unassailable part of Christian dogma, how Galileo slowed down time to determine how fast objects fall, and why Isaac Newton erased every mention of one man's name from his magnum opus Principia. You'll also figure out what Einstein meant when he insisted that space is curved, whether there is really such a thing as antigravity, and why some scientists think that the best way to get to outer space is by taking an elevator.

Gravity's ARC: The Story of Gravity from Aristotle to Einstein and Beyond


 
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?
 
Answer: We use the formula F=(G m1m2)/d2 because the satellite isn’t near the earth’s surface.  Now you just substitute in what you already know.
            F= [(6.67 x 10-11 Nm2/kg2) (1000 kg) (5.9742 x 1024 kg)]/ (500000m)2
            F=1.59 x 106 N

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Melissa Lagace