When and where on Planet Mars are the Sun's rays the most blueshifted?

Question

Let's say for a moment that the spin of a planet causes the Sun's rays to be blue-shifted in the morning.

As far as I know, redshift occurs in steps of like 2.6 km/s or something like that. We can't detect redshift except in steps of at least this size for some unknown reason. And so unless the earth is spinning that fast, we wont even incur a single step. But still something could be happening.

Lets say this very subtle, microscopic variation somehow has a significant impact on a planet over the course of millions or billions of years.

My question then is: when and where on on Planet Mars would be the highest blueshift in the Sun's rays? Clearly to me its going to be in the morning. In the morning at the equator is going to be at least one of the places.

But at what time of year?

And does this time follow a line north and south around the planet?

Or is there a specific moment and place where it is highest for some reason? Like the morning of the spring equinox at the 30 degree north latitude or something? If we know blueshift will be highest on the morning of the spring equinox... then at what latitude?

Answer 1

Just to add to the existing established relativistic doppler shift is a continuous process. The equation is on the order of:

$$1 + z=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$

Which contains no quantizing terms.

The notion of redshift quantization (very neat! Thanks for telling me about this!) is only based on a few observations, whereas continuous redshift has been observed in the other 70+ years of results. To quote https://briankoberlein.com/blog/seeing-red/

What we found was that the ideas of Arp and Tifft don’t agree with observation. What once hinted at redshift quantization is now seen to be due to a clustering of galaxies. When large number of galaxies or quasars are analyzed, the quantization pattern fades.

Answer 2

This is largely dependent on the radial velocity of the orbit of Mars, since its eccentricity is pretty large.

Radial velocity is maximised at a distance of:

$$r = \frac{r_P(2a - r_P)}{a}$$

Where $r_P$ is perihelion distance and $a$ is the semi-major axis.

This part of the orbit is 156 days before perihelion.

At this distance, the radial velocity of Mars should be 2,258 m/s, by far more important than the maximum surface velocity of 241.2 m/s at the equator. The range of the Sun-radial surface velocity doesn't vary much through the year either. Worst case, it's as low as 218.4 m/s due to the axial tilt of 25.19°, and of course it's even lower at other latitudes.

Given than small 23 m/s range of the surface velocity, the time would have to be between 141 and 172 days before perihelion in any case before looking up the equinox times. (edit: it looks like the autumnal equinox of Mars is roughly 70 degrees before Perihelion, so not very far form the maximum radial velocity point (89.97 degrees). The range is thus much narrower)

At the equator, very close to the maximum radial orbital velocity point would be the highest blueshift.