Quick gravitation question

1. Jul 30, 2009

TheDoorsOfMe

What does strength mean exactly in this context below. Is this the acceleration imposed by M on m?

Strength of gravitational field created by a mass M: g = F/m = -G(M/r^2)r^unit

2. Jul 30, 2009

rock.freak667

Newton's 2nd law: F=ma => a= F/m. So g = -GM/r2 is an acceleration due to gravity.

3. Jul 30, 2009

cepheid

Staff Emeritus
As you can see from the definition, the gravitational field strength is being defined as having dimensions of force per unit mass. In other words, a way of characterizing the gravitational field strength at a point in space is to say that if I put a "test mass" of 1 kg at that point in space, what force will it experience? (Or, an equivalent question: what will its acceleration be?). So you can see the usefulness of dividing out the mass of the test mass (or, equivalently, setting it equal to 1 kg). Evaluating the force on a "per kilogram" basis (i.e. evaluating the acceleration) means that if we see that a test mass at point A experiences a larger force than the same test mass at point B, we can definitely conclude that the gravitational field is "stronger" at point A than it is at point B.

Gravitation is a mutual interaction. Any two masses will interact through the gravitational force. What this means is that the first mass (M) will exert a force on the second mass (m). Likewise, the second mass (m) will exert an equal and opposite force on the first mass. The presence of both masses is required for any sort of interaction to occur.

4. Jul 30, 2009

TheDoorsOfMe

Thank you very much!

5. Jul 30, 2009

TheDoorsOfMe

one more:

"where r is the distance between the two masses and rˆis the unit vector located at the position of m that points from M towards m."

How can this vector be positioned at m and point from M to m?

6. Jul 30, 2009

TheDoorsOfMe

I feel like it should be the unit vector points from m to M and positioned at m.

7. Jul 30, 2009

cepheid

Staff Emeritus
Not sure I understand your question. A vector can be placed wherever you want, and oriented however you want, in general. The point is that the gravitational force always points *radially inward* i.e. towards the centre of the mass that is doing the gravitating.

The point is that that gravitational force acts ALONG the line connecting the two masses. This constrains its direction. WHERE you draw the vector along that line is not that relevant. You can slide it along that line to any place that suits your convenience (for the sake of your diagram).

EDIT: This is for point masses (masses that can be considered to be concentrated at a single point in space). If you are talking about some sort of extended body (one that takes up more than a single point in space) like an actual object, then the positions of the force vectors do matter and do have physical meaning: they tell you precisely where on that body the force is acting. But that doesn't change the fact that two forces of the same magnitude that lie along the same "line of action" will have an equivalent effect.

Last edited: Jul 30, 2009