Thoughts on gravitational redshift
[ I don’t claim to be scientifically accurate here, just collecting my thoughts ]
As a photon shoots out from the sun towards earth (or elsewhere), its distance to the sun increases rapidly as it approaches our planet. The effect of any force exercised by the sun would decline by the square of the distance — but it is never zero. It follows an inverse square law:
Fₛ= Mₛ/(d-r)² (where Mₛ is the mass of the sun: 1.989 × 10³⁰ kg, d is the distance between sun and earth: 148.4 million km and r is the distance between the sun and the photon as it travels to earth)
As it approaches the earth (i.e. r gets closer to 148.4 million km), the force exercised by the earth increases:
Fₑ = Mₑ/r² where Mₑ is the mass of earth 5.972 × 10²⁴ kg.
Combined (disregarding the influence of any other masses in the universe) we have: F = Fₛ - Fₑ = Mₛ/(d-r)² - Mₑ/r²
If we solve for x at the turning point where the earth exerts the same force as the sun, we get x~256693 km (856ms before reaching us). Investigating around this point, we see the following:
Comparing this halfway distance to other physical distances:
In 1911 Einstein estimated a redshift of 2 millionths of a wavelength; the original source is here:
Could we approximate that by purely looking at the relative (estimated) mass of earth and sun?
Does effective redshift (the balance between initial redshift when moving away from the sun, then blueshift when approaching earth) depend on the distance (and time) traveled?
Einstein’s formula does depend on the distance, as illustrated here:
As described here, scientists have determined the relative masses of the earth and the sun by relying on Newton’s laws. This can be more challenging for objects that are further away where one does not revolve around the other.
Using gravitational potential which reasons from the perspective of the greatest mass (it takes energy to overcome the difference in potential, as in ‘lifting’ the photons from the higher mass sun towards the lower mass earth) ignores the mass of the earth. For example, researchers have done spectral analysis on sunlight arriving to earth via reflection by the moon.
In contrast, a force based approach depends on the ratio of both masses but is independent of the distance / time of travel.
Consequently, a blue shifted spectrum would be explained as coming from a star that is lighter than earth. Which doesn’t exist in conventional cosmology.