Circular and Satellite Motion - Mission CG7 Detailed Help

An astronaut is on the orbiting Space Shuttle, approximately 60 miles (~100 000 meters) above the surface of the Earth. (The Earth's radius is ~6 360 000 meters and its mass is ~5.98 x 10^24 kg.) At this location, one might predict the acceleration of gravity to be ____.


 
Acceleration of Gravity or Gravitational Field Strength:
The acceleration of gravity at any given location near or above a planet's surface is often referred to as the gravitational field constant of that planet. Such acceleration values are directly proportional to the planet's mass and inversely proportional to the square of the distance from the planet's center.


 
The gravitational acceleration experienced by a person is inversely related to the separation distance between the person and the Earth's center. As objects get further from Earth' surface, the gravitational acceleration decreases. A distance of 60 miles above the Earth's surface is a very small distance compared to the distance from Earth's center to Earth's surface. The values in this question are provided, so the math can be pondered. At 60 miles up, an astronaut is about 6460000 meters from Earth's center compared to the 6360000 meters when on Earth's surface. This is a 1.6% increase in the distance from Earth's center. Using the inverse square law, this increase in distance would lead to a 2.5% decrease in the gravitational acceleration.


 
The acceleration of gravity (g) is the acceleration an object experiences when the only force acting upon it is gravity. According to Newton's universal gravitation law, its value can be predicted by the following equation:
 
g = G • Mplanet / d2

where Mplanet represents the planet's mass and d represents the distance that the object is from the planet's center.


 

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