### Question

Where in the United States is the force of gravity the strongest?

Asked by: Hanni Pilz

### Answer

According to the Newton's Law of Gravitation:

F=(GMm)/R^{2}=mg

Where G is the gravitational constant, M is the mass of the Earth, m is the mass of
the object, and R is the distance between the of the two objects (in this case, the
distance is between you and the center of the Earth.)

Therefore it could be assumed that the closer you are to the center of the Earth
(the lower the elevation), the stronger the force of gravity.

If I remember correctly the lowest place in the U.S. is Death Valley at -282 ft
(-85.9536m). Given that the mean radius of the Earth is 6.37*10^{6}m, we could
calculate g, acceleration due to gravity, in Death Valley using the equation above:

g=((6.673*10^{-11})(5.98*10^{24}))/(6.37*10^{6}-85.9536)^{2}
=9.834565215 m/s^{2}

Where G=6.673*10^{-11}

M=5.98*10^{24}

Compare this to the gravitational field calculated using the mean radius:
9.834299811 m/s^{2}

As you can see, the difference is so small, it is insignificant.

Answered by: Loren Chang, Physics Undergrad Student, UC Irvine