# what force of gravity do I exert on the Earth

Hello

According to Newton's Universal law of gravitation then you can calculate the force of gravity between 2 objects and the distance between them.

So it follows from this (and the 3rd law) that if the Earth pulls on me by 600N then I pull on the Earth by 600N. Correct?

And presumably i move to the Earth because i am less massive and have far less inertia than the Earth?

How does w = mg relate to the formula Fgrav = GM(1)M(2)/d^2
Can you derive the acceleration due to gravity g from these formula?

thanks
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EngineerCommented:
Since mass of the earth is constant and distance from the centre of the earth is "practically" constant G, M1 and d2 are constant and together constitute g and this g is multiplied with M2

so mg
Commented:
F = mg   is a special case of     F =  G*M1*M2/r²

If you are  m and M1,   then   g = G*M2/r²      where M2 and d are the mass and radius of the earth.
Commented:
gravity is a force between 2 objects.  The force is determined by both objects not just one.
So, there is only the one gravitational attraction between you and the earth,  not the earth's pull and your pull.

We commonly call the measure of gravitational force  "weight"

So,  if you weigh 100lbs  it's because you and the earth are pulling each other together with 100lbs of force.

w = mg

is

thus, if you know your weight (600N)  and you know your mass, you can calculate the accelration
Commented:
"So it follows from this (and the 3rd law) that if the Earth pulls on me by 600N then I pull on the Earth by 600N. Correct?"
correct     (you are obviously not overweight)

"And presumably i move to the Earth because i am less massive and have far less inertia than the Earth?"
correct

Consider the gravitational force two lead balls. Obviously by your reasoning the force on each has the same magnitude (the masses do not have to be the same.)
Now consider you and the earth (hen you are 1 cm above a floor.) This system is the same as the two lead balls.
Of course you will not stay 1 cm above the floor but you will soon drop to the floor whereupon the floor will exert a force on you which just cancels the gravitational force, so that you are now at rest.
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as an interesting sidelight, it was reported (probably unreliably) that the US government did a study to see that if the Chinese got all their population to run west off a table at the same time would they affect the rotation of the earth.

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Commented:
The gravitational force between you and the earth is the same -- it is just one force pulling two masses together.
The amount of the acceleration that results from this force depends additional on the masses of the two objects. So yes, you accelerate the earth to you as well, but this acceleration is so small (a=F/m) as the mass of the earth is so huge that it might not even be measurable.
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