# Physics

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Let's say that the force of gravity on the equator of the Earth is 9.81 m/s^2 what is the magnitutde of gravity of something at 41.603221,-73.087749 ????

I'm guessing that 41.603221,-73.087749 is lattitude and longittude so I really have no idea what to do.

The question asked me to find the magnituted of gravity on the equator and the find the magnitutde at that point...

I don't know how to find the magnitutde at that point that's what I'm having problems with

• Physics -

There are effects due to varying density of the earth at different points and the non-spherical shape of earth but they are tiny. Assuming the radius is constant and the center of mass is at the center, there is no effect of latitude or longitude on gravity itself. However there is an effect of latitude on the apparent gravity due to centripetal acceleration, w^2 r outward from the axis of rotation through north and south poles. I am using w for omega, the angular velocity of earth in radians per second. As you go North (or South) from the equator r decreases from the radius at the equator as r = R cos (Lat)
w is 2 pi radians / (24*3600) seconds
The resulting acceleration is outward from the axis so its component outward from earth center is
w^2 R cos^2 (Lat)
g = g due to earth mass - w^2 R cos^2 (Lat)
At the equator where Lat = 0: 9.81 = g due to earth mass - w^2 R
So: g due to earth mass = 9.81 + w^2 R
calculate that g due to earth mass
then at some other latitude you can get your apparent g from
g = g due to earth mass - w^2 R cos^2 (Lat)

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