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Suppose a copy of Earth. This planet can travel at any arbitrary speed, and it's set to travel along the galaxy's spiral arms. It rotates counterclockwise, at the rate of 24 hours a rotation. It keeps its standard gravity and atmosphere regardless of its travelling speed.

The observer is standard average human, standing at a fixed point on the equator, using their own naked eyes. Clear sky, no clouds, no light pollution, no loopholes. With rotation, our observer will first pass through the side facing forward, from midnight to midday.

Now I'm going to make some assumptions, feel free to correct them if they're offbase.

If an object moves fast enough, I'm pretty sure that blueshifting and redshifting should happen.

What I expect (or perhaps wishfully think) is that over the course of a rotation our observer would see the stars get gradually bluer until about 6am, then whiter until midday, then redder until 6pm, then whiter until midnight.

What's the minimum travelling speed for such blue/redshifting to be noticeable and visible to our observer?

The question is about the travelling speed (of the planet going forward), not the rotation speed (which is fixed at 24h/rotation). Answers prefered in fractions or percentage of $c$, precision to the order of magnitude is sufficient.

Edit: Here's a diagram from @Tortliena that illustrates the situation

A diagram of the movement and rotation

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  • $\begingroup$ If you don't define how sensitive is the observer, this cannot be answered. $\endgroup$
    – L.Dutch ♦
    Oct 7, 2022 at 9:48
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    $\begingroup$ @L.Dutch Sensitive like a standard average human with two eyes? $\endgroup$
    – AmiralPatate
    Oct 7, 2022 at 9:49
  • $\begingroup$ what you are describing is a change in the redshift due to the angular speed of the planet. this is absolutely minimal and the same on our earth as on any other 24h planet no matter at which speed it moves. $\endgroup$
    – ths
    Oct 7, 2022 at 9:53
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    $\begingroup$ @ths I envision the change to be due to the position of the observer. At one point during the day, you're on the side hurling towards the stars. 12 hours later because of the rotation, you're on the side hurling away from the stars. $\endgroup$
    – AmiralPatate
    Oct 7, 2022 at 10:02
  • $\begingroup$ yes. but the difference is only ~3300km/h. $\endgroup$
    – ths
    Oct 7, 2022 at 11:14

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How big redshift You need?

$z=\sqrt{(c+v)/(c-v)}-1$

z = redshift v = speed c = speed of light

IIRC for non trained human is around .6c for trained astronomer around .2c but we can make devices to see even less than 1km/h difference for NEO

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    $\begingroup$ Why is it so different with astronomers? Do regular starsighting really change how easily you can distinguish colors? $\endgroup$
    – Tortliena
    Oct 7, 2022 at 11:34
  • $\begingroup$ Tortliena if have 2 colors next to eo then no problem but when have dot on black to compare to dot on black who has been seen 6 hours ago is diffrent. Training will give You much. $\endgroup$
    – Kamitergh
    Oct 7, 2022 at 12:41
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Exactly the same as Earth

If the goal is for the observer to notice a change in redshifting over the course of the day, then the only speed that matters is: how fast is the observer moving "forward" during one part of the day, compared to how fast they are moving "backward" during the other part of the day.

This will be completely determined by the planet's rotation. It will not matter whether the planet is traveling at the speed of light or is completely stationary.

The numbers we care about are the rotation period and the radius. If those numbers are the same as Earth, then the blueshift and redshift your observer sees will be the same as we see here on Earth.

The internet says that an object on the Earth's surface travels through space at 465 meters per second. If that's true, then the greatest delta will be twice that: 930 m/s.

Thus, the amount of redshifting due to the planet's rotation will be however much redshifting occurs from traveling at 930 m/s.

930 m/s seems like a lot of speed, but I guess it's not. I know this because I have looked at the sun and the stars, and they have never looked either redshifted or blueshifted to me (and I have normal color vision).

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  • $\begingroup$ According to the doppler effect I kinda doubt only rotation speed make redshifts here. It's exactly like if you were next to a sign and a honking car passes by : They will sound distorted. Now change the perspective : sit in the car (ie. rogue planet), give big honks to all signs (stars) on the road, the signs will sound distorted. Excluding all weird gravitational stuff, that's roughly the querent's situation :). $\endgroup$
    – Tortliena
    Oct 7, 2022 at 16:37
  • $\begingroup$ @Tortliena Yes, but that shift will not change over the course of the day, which is OP's specific request: "over the course of a rotation our observer would see". Whether other stars or galaxy are red- or blue-shifted will not change based on what time of day it is, aka the observer's position on the planet surface. $\endgroup$
    – Tom
    Oct 7, 2022 at 17:21
  • $\begingroup$ I think I get the difference between our viewpoint : you see the lightshift on the same star over time, while I see it like "it's midnight, what are the stars dominant colors on this side of the planet?" The question is a bit ambiguous on that. $\endgroup$
    – Tortliena
    Oct 7, 2022 at 17:31
  • $\begingroup$ To clear the ambiguity hopefully, my question is essentially if you lay down on the grass for 24h and look straight up, do the stars you see (which would be different) cycle color over the 24h? It isn't whether star X is always the same color. $\endgroup$
    – AmiralPatate
    Oct 12, 2022 at 8:02

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