Interacting gravitational fields

In summary, gravitational fields interact with each other by either adding linearly or requiring a numerical solution depending on the equations used. In "weak field" environments like the solar system, fields effectively add linearly in both Newtonian and General Relativity. However, in extreme environments such as neutron stars and black holes, non-linearity must be taken into account. The effects of warping on space are also difficult to generalize and must be numerically solved in most cases.
  • #1
Drops of Fire
5
0
How do gravitational fields interact with each other? Because the Earth is in the Sun's and the moon is in the Earth's and the sun's. I think ocean tides on Earth is an example of it, but is there anything more specific? What is happening to an area of space inside multiple gravitational fields?
 
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  • #2
In Newtonian gravity the equations are linear, so you simply add up the various individual fields to get the total field. In GR the equations are non-linear so you cannot simply add up the various individual field to get the total field. So even a simple two-body problem usually requires a numerical solution in GR.
 
  • #3
DaleSpam said:
In Newtonian gravity the equations are linear, so you simply add up the various individual fields to get the total field. In GR the equations are non-linear so you cannot simply add up the various individual field to get the total field. So even a simple two-body problem usually requires a numerical solution in GR.

For "weak field" environments like the solar system, fields effectively add linearly for GR as well. For accurate calculations (such as Mercury's perihelion precession) you have to take into account not only the Newtonian field acting on objects at rest but also additional effects caused by motion through curved space, but these additional effects are still proportional to the Newtonian field and still effectively add up linearly for multiple sources.

In practice, you only need to take non-linearity into account in extreme environments such as neutron stars and black holes.
 
  • #4
But what's happening to the space? If it warps one way, how to it react to warping another way?
 
  • #5
As I said above, unless you are close to the Newtonian limit, you basically just have to numerically solve the EFE for the situation you have in mind. The nonlinearities make it difficult to make general statements of the kind you are asking.
 

1. How do interacting gravitational fields affect objects in space?

Interacting gravitational fields can cause objects in space to experience forces that can either attract or repel them. This can lead to the formation of stable orbits or collisions between objects.

2. What causes gravitational fields to interact with each other?

Gravitational fields interact with each other because of the fundamental force of gravity, which is caused by the mass and energy of objects. Objects with larger masses have stronger gravitational fields and can influence the motion of other objects.

3. Can interacting gravitational fields cause changes in the fabric of space-time?

Yes, interacting gravitational fields can cause changes in the fabric of space-time, as predicted by Einstein's theory of general relativity. This is because gravity is not just a force between objects, but also a distortion of space and time.

4. How do scientists study and understand interacting gravitational fields?

Scientists study and understand interacting gravitational fields through observations, mathematical models, and experiments. They use tools like telescopes, satellites, and computer simulations to gather data and make predictions about the behavior of these fields.

5. Are there any practical applications of understanding interacting gravitational fields?

Yes, understanding interacting gravitational fields is crucial for space exploration, satellite communication, and predicting the motion of celestial objects. It also has practical applications in fields like engineering and navigation, where the effects of gravity must be taken into account for accurate calculations and designs.

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