The Value of Gravity g

The Value of gravity g

THE VALUE OF GRAVITY

An equation was given for determining the force of gravity F(_gravity) with which an object of mass m was attracted to the earth

F(_gravity) = m*g

But in this case, a 2^nd equation will be used to calculate the force of gravity with which an object is connected to the earth.(gravity)

While d is the distance from the center of the object to the earth center.

In the first equation above, g is referred to as the gravitational acceleration. Its value is 9.8 m/s² on Earth. That is to say, the gravitational acceleration on the surface of the earth at sea level is 9.8 m/s². When discussing the gravitational acceleration, it was mentioned that the value of g is dependent upon location. There are slight changes in the value of g about earth's surface.

These changes correspond from the changing density of the geologic formation under each particular surface location. They may be resulted from the phenomena that the earth isn’t totally spherical. Earth's surface is further from its center at the equator than it is at the poles. This would result in larger g values at the poles. the value of g changes as one body go away from earth's surface or into a location of orbit about the earth.

 

Value of Gravity (g) relies on the Location or the distance from the center of earth or other heavenly bodies.

To know why the value of g is so location reliant, we will use the two equations above to derive an equation for the value of g. The aforementioned, both mathematical expressions for the force of gravity are set equal to each other.

Now observe that the mass of the object (m) is residing on both sides of the equal sign. Thus, m can be canceled from the equation. This leaves us with an equation for the gravitational acceleration.

The above equation demonstrates that the gravitational acceleration is dependent upon the mass of the earth (approximately 5.98x10²⁴ kg) and the distance (d) that an object is from the earth center. If the amount 6.38 x 10⁶ meters (which is earth radius) is used for the distance from Earth's center, then gravity (g) will be deduced to be 9.8 meters/second⁽²⁾. Certainly, the value of gravity (g) will also change as an object is moved away of further from Earth's center.

For example, if a body of mass m  was moved to a location that is two time the earth's radius from the earth center - that is, two times 6.38x10⁶ m - then a considerably different value of g will be found. As shown below, at two times of the distance from the earth center, the values of g become 2.45 m/s².

 

Here is a comparison of gravitational field strength for different distances from the center of the earth.