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AndrewJ
2009-Mar-01, 12:43 AM
How does the Earth's gravity "achieve" the same acceleration of two objects of differing mass that are both at the same distance/altitude from it?

The more massive of the two objects would have a greater resistance to being accelerated than the less massive and require a greater force acting on it to accelarate it to a given speed (it would have more weight). How is the greater force activated? Does the presence of more mass within a gravity field prompt the exchage of more (virtual) force mediating particles? How would the greater force be caused in the model of gravity as mass-bent space?

Peter B
2009-Mar-01, 01:06 AM
The heavier object does indeed have greater inertia mass, and thus accelerates more slowly. But it also has greater gravitational mass, and thus accelerates faster. These two factors cancel out, meaning that all objects accelerate at the same rate.

Bob B.
2009-Mar-01, 02:16 AM
The force of attraction between two masses is given by the following formula,

F = G * (m1 * m2 / r^2)

G is the constant of gravitation and, let's say, m1 is the mass of the Earth. If the bodies in question are at the same distance from the Earth, r, then everything on the right hand side of the equation is a constant except for the mass of the body, m2. The magnitude of the force is, therefore, directly proportional to the size of the mass. If force and mass are in direct proportion to each other, then acceleration is constant.

AndrewJ
2009-Mar-01, 04:35 PM
The heavier object does indeed have greater inertia mass, and thus accelerates more slowly. But it also has greater gravitational mass, and thus accelerates faster. These two factors cancel out, meaning that all objects accelerate at the same rate.

Does the presence of more mas in the Earth's gravity field generate more force mediating particles? How would this work in the model of a gravity field as bent space?

grant hutchison
2009-Mar-01, 04:49 PM
Does the presence of more mas in the Earth's gravity field generate more force mediating particles? How would this work in the model of a gravity field as bent space?If we're imagining gravity as an exchange of gravitons, then it certainly seems plausible that more mass would generate more gravitons (or perhaps gravitons of higher energy?).
Using general relativity, all we need is for free-falling objects to follow geodesics in curved spacetime. Since the geodesic is the same for a small mass and a big mass, we automatically produce the same "gravitational acceleration" for the two masses, as measured by an observer who is stationary in the gravity field.

Grant Hutchison

WaxRubiks
2009-Mar-01, 04:52 PM
I suppose if a small object is following a straight line in space-time, when it falls towards Earth, then Earth must also be following a straight line through space-time, as it falls towards the small object.

AndrewJ
2009-Mar-01, 05:09 PM
If we're imagining gravity as an exchange of gravitons, then it certainly seems plausible that more mass would generate more gravitons (or perhaps gravitons of higher energy?).

Great. That's what I was hoping to hear.

Using general relativity, all we need is for free-falling objects to follow geodesics in curved spacetime. Since the geodesic is the same for a small mass and a big mass, we automatically produce the same "gravitational acceleration" for the two masses, as measured by an observer who is stationary in the gravity field.

Similar to how the same downhill equally accelerates both a low-momentum smart car and a truck, I suppose.

cjameshuff
2009-Mar-04, 12:08 AM
How does the Earth's gravity "achieve" the same acceleration of two objects of differing mass that are both at the same distance/altitude from it?

Take two identical objects and drop them from the same height...they fall at the same rate, as expected. Now tie or glue them together...would you expect them to fall at a different rate when bound together than they would fall at when dropped separately? Falling separately, they would not change position relative to each other, so what force could they exert on each other through the binding to make them both fall faster or slower?

AndrewJ
2009-Mar-04, 04:13 AM
Take two identical objects and drop them from the same height...they fall at the same rate, as expected. Now tie or glue them together...would you expect them to fall at a different rate when bound together than they would fall at when dropped separately?

Everything, bound or separate, would initially be accelerated toward the gravitational source at the same rate. To answer the question, the (more massive) bound object would ultimately fall to Earth faster as proportionally less of its momentum would be lost to air resistance and atmospheric friction.

Falling separately, they would not change position relative to each other, so what force could they exert on each other through the binding to make them both fall faster or slower?

I have read this several times and cannot see the point you are making.

cjameshuff
2009-Mar-04, 06:52 AM
I have read this several times and cannot see the point you are making.

You asked how gravity "achieved" equal acceleration of objects of different mass. A large object can be viewed as two smaller objects bound together. There is no reason to expect the fact that they are mechanically attached to each other to affect the rate at which they fall, and so there is no reason to expect the attached pair to fall faster or slower than either part would fall alone.

Air resistance is another issue entirely. Equal accelerations are not predicted in the presence of significant aerodynamic forces. There is also a difference when the objects are not at the same height in the gravity well...tidal forces are involved in that case, but the question fortunately specifically excluded that case.

AndrewJ
2009-Mar-04, 04:34 PM
A large object can be viewed as two smaller objects bound together. There is no reason to expect the fact that they are mechanically attached to each other to affect the rate at which they fall, and so there is no reason to expect the attached pair to fall faster or slower than either part would fall alone.

So we might say gravity works the same on every kilogram whether its a separate entity or bound to others.

grant hutchison
2009-Mar-04, 04:52 PM
So we might say gravity works the same on every kilogram whether its a separate entity or bound to others.Yes. Like the centrifugal and Coriolis pseudoforces, gravity is measured in newtons per kilogram, not in newtons.
That's why the textbooks quote an "acceleration due to gravity" at the Earth's surface, rather than a force.

Grant Hutchison

Gandalf223
2009-Mar-04, 06:38 PM
How does the Earth's gravity "achieve" the same acceleration of two objects of differing mass that are both at the same distance/altitude from it?

Simple. Gravity is defined as an acceleration; mass does not enter into the equation.

For the earth: g = 9.8 m/s2