# Are the forces of gravity subject to the Doppler effect?

Was it considered that the force of gravity could vary according to the redshift equation?

$$1+z=\frac{1+v \cos (\theta)/c}{\sqrt{1-v^2/c^2}}$$

If those who consider this are right, then it would imply that an object leaving a gravitational system would experience a slight decrease in the gravitational force from behind, and an object entering a gravitational system would experience a slightly increased gravitational force in front of it. Therefore, an object flying-by the Earth would experience a gravitational field that is slightly ahead it even if it is at the apex of its trajectory.[Note 1]

Also, if the object were to travel between latitudinal lines, in the same direction as the planet's spin, then a transverse Doppler effect would reduce the force of gravity from latitudes further from the equator more so than they would for latitudes closer to the equator, resulting in a slight gravitational pull towards the equator, giving it a lower effective potential.[Note 2]

If such were to occur, is this something that can be accommodated by General Relativity?[Note 3]

1) Could that not explain the anomalous precession of the perihelion of Mercury, Venus, etc.?
2) Could that not explain the flyby anomaly?
3) ...I'm not expecting that it will.

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bcrowell
Staff Emeritus
Gold Member
If those who consider this are right, [...]
Does "those who consider this" mean you?

No, you can't just randomly apply the Doppler correction formula to randomly chosen physical variables.

Does "those who consider this" mean you?

No, you can't just randomly apply the Doppler correction formula to randomly chosen physical variables.
So the forces of gravity are not subject to the Doppler effect? Or are you just saying that you cannot randomly apply the Doppler effect to the forces of gravity, i.e. haphazardly?

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jtbell
Mentor
The Doppler effect applies to frequency and wavelength. How does it apply to forces? The Doppler effect applies to frequency and wavelength. How does it apply to forces? Frequency and wavelength apply to the photon. The photon is a gauge boson. It is a particle which allows for the transfer of energy from one body to another through a fundamental force, and in this case that fundamental force is electromagnetism. The magnitude of amount of momentum which a mass-bearing object receives from a photon is given by the relation $$p=\frac{h}{\lambda}$$, where $$p$$ is the momentum of the photon, $$h$$ is Planck's constant, and $$\lambda$$ is the wavelength of the photon in the frame of reference of that mass-bearing object.

So we know of at least one type of force (electromagnetic), which is mediated through a type of field (an electromagnetic field), clearly obeying the relativistic Doppler formula.

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atyy
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I am not sure but it can apply to gravitational waves but not gravitational forces.

The Doppler shift has two parts, the classical part which is your velocity makings wave crests appear to run by you faster or slower. There's also a relativistic component involving the time dilation.

Assuming you were heading toward a source of (low amplitude) gravitational waves, the same Doppler shift would apply as does for light waves.

The general phenomenon is not limited to waves only, it's just that it was discovered that way. But it's perfectly reasonable mathematically to extend the Doppler shift concept to non-wave fields.

[..]
The general phenomenon is not limited to waves only, it's just that it was discovered that way. But it's perfectly reasonable mathematically to extend the Doppler shift concept to non-wave fields.
Mathematically reasonable perhaps, but physically not - except if you can make it plausible that static fields have something like propagating wave crests that can be counted.