Can we measure the gravity of only one object?

Question

Today, in order to measure gravity we use the Newton's formula which is always between two objects. However, can we measure the curvature of spacetime caused by a single object? For instance we use "g" as the acceleration caused by earth. Why arent we measuring the same thing with other objects as well?

Answer 1

> "we use "g" as the acceleration caused by earth. Why arent we measuring the same thing with other objects as well?"



We are. Newton's formula measures FORCE (Newtons). But it can just as easily be used to measure "field strength" (Newtons per kilogram). The field strength is a property of the space around a massive object, and doesn't depend on the mass of the secondary object. For example, of you have an (isolated) 100 kg mass, you can say the the gravitational field strength, at a location of 100 meters from that mass, is 6.67×10^-9 Newtons per kg. this field strength is independent of any particular secondary mass that may or may not be brought into the vicinity of the 100 kg mass.

Answer 2

First off, don't use g as the acceleration of gravity. g is free energy.... use a sub g... for acceleration due to gravity. Secondly you can find the "gravity" of any object. What I am assuming you are looking for is the gravity "field" of an object. Well just like the force of an interaction between two charges is Fe= K q(sub 1) q(sub 2) / r^2 and the field of a single charge is E= K q(sub 1) / r^2 the equation for the force of gravity on an object is Fg= G m(sub 1) m(sub 2) / r^2 so the equation for the gravitational field of an object is G m(sub 1) /r^2 But because the gravitational field is related to mass this is also the acceleration that any object would experience due to this field.

Answer 3

Nope, can't be done. It takes two to tango when it comes to gravity force: the source M of the gravity field and the target m the field acts on. And that's why weight W = mg = mGM/r^2...even when we invoke the general theory of relativity and its curved space.



Note that g = GM/r^2 is independent of the target mass. So we can certainly use g to measure the weight of other targets as long as the source mass M is the same mass. We would need to adjust the value of g for the distance from M however.



But the source in the GTOR can be mass, energy, and/or stress (force over a volume of space). Even so, there must be a target, the thing with the weight, that is caught in the potential energy well created by the curvature of space.



Of course you can have a source with nothing to act on, but then there wouldn't be a force would there? And as soon as you stuck a measuring device into the field, that would become the target mass m.