Originally Posted by

**Tony2021**
**fig5**

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Originally Posted by

**Tony2021**
The smaller the eccentricity, the closer the orbit is to a circle, the more susceptible the orbit is to external interference, and the more likely it is to precess.

I don't see how this could be the case other than if the precession is a pseudorotation (a type of motion that gives the appearance of a rotation but isn't actually a rotation).

Originally Posted by

**Tony2021**
1. How are gravitational waves caused?

2. Will the revolution of the sun cause gravitational waves?

I should point out that my understanding of gravitational radiation may differ from the commonly held view in a number of ways, and in particular that I disagree with the commonly held view that a rotating rigid dumbbell emits gravitational radiation.

To answer the question of how gravitational radiation is produced, consider the case of two gravitational objects in mutual orbit. It is commonly assumed that it is the orbital motion that produces the gravitational radiation, but it is actually the inward radial motion that produces the gravitational radiation. The inward radial motion and the emission of gravitational radiation are concomitant, so it is not quite correct to say that the inward radial motion causes the gravitational radiation, or that the gravitational radiation causes the inward radial motion. But the inward radial motion changes the gravitational field that surrounds each object, and this change in the gravitational field results in a propagation of gravitational radiation away from the two objects. It should be noted that gravitational radiation is distinguished from the gravitational field in that gravitational radiation decreases at a lesser rate with respect to distance. Therefore, at great distances from the objects in mutual orbit, gravitational radiation will be the dominant form of gravitation.

For the second question, if by "revolution", you mean rotation about its spin axis, then no, rotation of the sun does not cause gravitational waves. This is the commonly held view by the way, not just my own view. Spinning objects that possess axial symmetry do not emit gravitational radiation. My own view expands upon this in that a spinning rigid object of any kind does not emit gravitational radiation. In general relativity, a spinning rigid object is actually

**stationary**, and the spacetime surrounding it is also stationary. Therefore, there cannot be emission of any radiation, which would lead to

**changes** in the emitting object. Unfortunately, I am unable to

*prove* that there is no drag that slows the rate of rotation, but I can say that such a slowing of the rate of rotation would violate the conservation of angular momentum in a way that the emission of gravitational radiation would be unable to accomplish.

I should also add that spherically symmetric gravitational radiation cannot exist, and that any change in the distribution of matter that maintains spherical symmetry (eg an expanding or contracting ball of matter) does not emit gravitational radiation.

Originally Posted by

**Tony2021**
3. Will gravitational waves affect the surrounding gravity?

I'm not sure what you mean by this question. Gravitational radiation and the gravitational field are locally the same type of spacetime curvature. For weak gravitational radiation in a weak gravitational field, the total field is a linear sum of the two fields; but for strong fields, the combination of the two fields is non-linear (although this might be an artefact of the peculiar nature of spacetime curvature).

Originally Posted by

**Tony2021**
4. Does gravitational wave have Doppler effect?

I should remark that solutions to wave equations are not necessarily sinusoidal waveforms, and one shouldn't regard "waves" as necessarily sinusoidal waveforms. However, any waveform can be decomposed as the sum of sinusoidal waveforms of various frequencies. But in general, a gravitational wave is a non-linear combination of component waveforms, so it is not clear how readily one can speak of component frequencies except in the case of weak field radiation (where the combination is linear).

Anyway, the Doppler effect is not a property of the particular field, so the Doppler effect applies to gravitational waves as it applies to other waves (although the question of whether the wave propagates at the speed of light does need to be considered... in the case of weak field gravitational radiation, it does propagate at the speed of light).

Originally Posted by

**Tony2021**
5. Is the density of gravitational waves under the Doppler effect uneven?

I don't understand this question.