Expert: Philip Stahl - 9/18/2008

Question
This question is probably easy for you but I am completely confused. Science isn't exactly the strongest aspect about me. The question for the mass of the Sun has the big G. Does that represent the exact value of gravity or a constant that balances the question? Also, if someone jumps off a chair, isn't the Earth's gravitational force on her same as her gravitational force on Earth? or would it be higher?
Thank you for your time.

Answer
Hello,

From what I can glean from your query, you are confusing two different things here: the universal gravitational constant ("big G") and the gravitational acceleration ("g"). One is related to the other by the equation (say for the value of g for a body of mass m attracted to the Earth)

g = GM/r^2


where r is the distance between mass and center of Earth.

In respect of your last question, what you are really asking about is the validity of Newton's third law of motion - usually expressed in every day terms as "for every action there is an equal but opposite reaction".

Or more explicitly in symbolic form:   F(AB) = - F(AB) or F(AB) = F(BA)

that is, the force that body A exerts on body B is equal and opposite to the force that body B exerts on body A.

So, in this sense, the force of attraction between a mass on Earth (A) is equal to the force of attraction of the Earth on the mass. (Or to put it another way, the acceleration of m toward M, the Earth, is equal to the acceleration of M toward m, the body). Whether one 'jumps' off a chair or not is immaterial since the value of g - at the jumper's location-  doesn't change.