Gravitational Force: Determining Relative Accelerations

In summary, in an accelerating reference frame, a pseudo-force must be added to compensate for the acceleration, and this can be applied to determine the acceleration of a planet in relation to another planet in the same frame. However, when looking at the same scenario from an inertial frame, the acceleration of the frame and object would add to determine the apparent acceleration in the accelerating frame.
  • #1
sheriefer
2
0
(This isn't a homework problem, just something I've been thinking about.) Suppose we have two planets isolated in space separated by a distance "D." They exert a gravitational force on each other which changes as they get closer. If we were in the accelerating reference frame of one of the planets, how would one determine the acceleration of the other planet? Of course the acceleration is not constant and would be dependent on their distance. Relative accelerations don't add like relative velocities in the Galilean transformations, correct? Can you satisfy my curiosity?
 
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  • #2


Hi, sheriefer.

In an accelerating reference frame, you can add a pseudo-force to everything to compensate for your acceleration -- otherwise Newton's equations are not valid. Essentially, if you wanted to work in the planet's reference frame, you would have to add a pseudo accelerating force to the other planet to accelerate it toward you at the rate you were accelerating toward it, then also add the gravitational acceleration.

If you have an accelerating object from the point of view of an inertial reference frame, then look at it from an accelerating reference frame, let's say accelerating in the opposite direction, the acceleration of the frame and object would add for the apparent acceleration in the accelerating reference frame, if that's what you mean.
 

1. What is gravitational force?

Gravitational force is a fundamental force of nature that describes the attraction between objects with mass. It is responsible for the motion of planets, stars, and other celestial bodies in the universe.

2. How is gravitational force calculated?

The strength of gravitational force between two objects is determined by their masses and the distance between them. The formula for calculating gravitational force is F = G (m1m2)/d^2, where G is the gravitational constant, m1 and m2 are the masses of the objects, and d is the distance between them.

3. What is relative acceleration?

Relative acceleration is the difference in acceleration between two objects. It is used to describe the motion of one object in relation to another, and can be affected by external forces such as gravitational force.

4. How does gravitational force affect relative accelerations?

Gravitational force affects relative accelerations by causing objects to accelerate towards one another. The acceleration of an object due to gravitational force is directly proportional to the mass of the object and inversely proportional to the square of the distance between them.

5. How is gravitational force used to determine relative accelerations?

Gravitational force can be used to determine relative accelerations by calculating the force between two objects and using Newton's Second Law of Motion, which states that the net force on an object is equal to its mass multiplied by its acceleration. By comparing the gravitational forces on two objects, their relative accelerations can be determined.

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