Circular and Satellite Motion - Mission CG7 Detailed Help

The acceleration of gravity (g) value for an object of mass 'm' located on the surface of some planet of mass 'M' and radius 'R' is ____ related to the ____. List the two that apply ... .


 
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 acceleration of gravity (g) is the acceleration an object experiences when the only force acting upon it is gravity. The force of gravity would be the net force and the acceleration would be the force of gravity divided by the object's mass.
 
g = Fgrav / mobject

Substituting Newton's expression for gravitational force into the numerator would result in a new equation for the acceleration of gravity which is applicable to locations other than on Earth's surface:
 
g = ( G • mobject • Mplanet / d2 ) / mobject
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.


 
Many students have the conception that the acceleration of an object acted upon by gravity is dependent upon the object's mass. After all, the acceleration is calculated as the ratio of net force to mass. But don't be fooled. In the case of a free-falling object, the net force is also dependent upon mass. As shown in the derivation in the Formula Frenzy section, the mass of the object cancels from numerator and denominator. The acceleration of gravity value is independent of the object's mass. All objects free fall at the same rate of acceleration.


 

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