Speed is relative, right, so there has to be some point for an object to relate to, to determine the speed of it.
Geostationary satellites are moving at speed but are stationary relative to Earth, so how is their speed determined?
The Voyager spacecraft are travelling something like 17kms, what is that in relation to? Out in space everything is moving so what reference point can be used to determine their speed?
Don’t need answer fast 
The satellites are easy - since they are stationary above a spot on the earth, they must make one rotation around the earth in 24 hours. The distance above the surface of the earth is also known, since there is only one altitude where the rotation take exactly one day.
As for Voyager - it’s speed is determined through various means, including doppler shift of the radio signals it transmits, and the calculation of it’s acceleration due to how much propellent has been burned. Also, space probes can measure their speed relative to the “fixed stars,” which are far enough away that they can be assumed to be at a fixed, infinite, unmoving reference point.
And Voyager’s speed is calculated in relationship to Earth. For that calculation we’re geocentric; since we’re observing from Earth we provide the speed “as seen from Earth”. We could also calculate its speed in relationship to the Sun, or say that it’s stationary and that we’re moving at 17km/sec, but neither of these would provide more-useful information and they’d be more complex (one mathematically, one mentally) so we don’t bother.
So if two light particles with no other reference then each other went in opposite directions, they would still measure each other as only traveling apart at the speed of light rather than 2c. But the same thing would happen if they set off perpendicularly. Would there be any meaningful way to tell these two situations apart without a third observer?
As already noted, the speed of an orbiting object is the most straightforward to measure because it’s simply a function of the circumference of its orbit and its orbital period. Whether a satellite is geostationary or not isn’t really relevant. Likewise, all satellites are moving with the earth around the sun, and with the sun around the galaxy, but that’s not usually relevant so isn’t included in the stated measurement.
For non-orbiting objects like Voyager, speed is just stated with respect to whatever reference point is the most relevant at any given time. With Voyager, this has been different at different times – initially, the most important reference point was its speed relative to Earth, then it was with reference to the various planets it was visiting. Now that it’s left all of that behind and is leaving the solar system, its speed is stated as “heliocentric recession speed” – relative to the sun, or in effect relative to the solar system as a whole.
How is speed in space measured?
One of the crewmen in your ship throws out a special device with light sails attached to it so that it stays relatively in one place. this is called a “log”, because at one time they used an actual piece of a dead tree. The crewman would let a line attached to the log run out between his space glove-covered fingers until a timing glass ran out (the timing glass would be placed in a special rotating housing, so that centrifugal force would act as artificial gravity; otherwise the sand particles would just float in the glass), at which time the line would be reeled back in. The distance traversed in that time could be determined from the length of line run out. This could be measured, but an adept crewman would already know how much line had passed by counting the number of regularly-spaced knots tied in the line he had counted. This gives the spaced velocity in “knots.”
The result would be recorded in the “Captain’s Log,” just like in Star Trek.
There is no privileged known or special reference frame. There is no objective “speed” outside of that measured to another object.
Add to that that no particles move faster than light in any reference frame excluding the effects like expansion.
The photons energy level would change and it would be shifted in the direction of blue but no observer would ever view any photon as going faster than light.
If you say, accelerate towards a particle of light it would shift from the visible spectrum it will shift up to x-ray or gamma-ray spectrum as you went faster but it would still appear to still be traveling the speed of light.
But your reference frame is just as valid as any other reference frame and we choose the center of the earth, solar-system or galaxy as a reference frame when discussing movement for our convenience to help with cognition but those frames are not any more privileged than any other reference frame.
So the only way to determine which direction a photon is traveling without a third reference would be by its color?
Also, wouldn’t the log example be impossible in space since the vacuum has no drag?
That’s why you use a light sail, so the light pressure retards the motion of the log.
And if you’re wondering how that slows it down when the light can potentially come from either direction, it’s up to the skill of the crewman. It’s all in the wrist.
Just don’t get a guy in a red shirt to make the measurement, because there’s an even chance he’ll just be sucked into the vacuum.
It doesn’t matter at all, you measure that speed from two particles. Speed is purely relative and yes the log would just be co-moving in a practical example.
The relative speed of two particles only depends on those two particles and to be more precise the measured speed is only accurate from your chosen particles point of view.
While it doesn’t apply much at practical speeds the “speed” of two objects is not necessarily invariant between those two particles.
It is a place where we need to ignore our human intuition.
As an example, if you are riding on a train and walking forward on the train, to an external observer besides the track your velocity is not simply the sum of your walking speed and the trains speed.
The difference is small but important. The third observer in your case is completely irreverent to the observations of the other two observers and is unneeded.
I should add that to make discussions easy within the limitations of human cognition there are several defined reference frames like the International Celestial Reference Frame.
But these frames are only special because they are chosen as a common reference frame to enable the communication of ideas and are not actually privileged over any other frame of reference outside of that value which they provide in communication.
There are reference frames that are special in more deeply significant ways than just being chosen as common references for communication. On a cosmological scale, there is a velocity between objects that is correlated with their current distance, which is another way of saying that the universe is expanding, and the Hubble constant is the proportionality constant in this correlation – but superimposed on this is a range of object motions for various specific reasons such as gravitational attraction. Thus the Milky Way and Andromeda galaxy are running toward each other at half a million mph (or was it kmph or mps?). OK, with this all in mind, there is a statistical average velocity for an observer to move at such that there’s no asymmetry in the recessional velocities in all directions for distant objects. An observer moving like this is in a reference frame that is special in the sense that it is average for the whole universe, and, in the limit, was arbitrarily stationary in the arbitrarily tiny universe momentarily after the big bang (and before the big inflation).
I’ve never heard of any theory that would let you detect this special reference frame without doing the study of relative velocities to distant objects, but there is a lot to be learned about cosmology. Who knows? Maybe there’s something fundamentally special about this frame. We don’t even understand dark matter and dark energy.
It’s worth mentioning here that rotation is not relative. There is one preferred non-rotational reference frame for every moving reference frame and any observer will be able to figure out the what the orbital speed is in that frame.
That looks a lot less profound and interesting than I think it is. I guess it requires more context.
No, no, it’s cool.
To add to this and to clarify a part that I think may be misleading to some readers.
The Galactic rest frame and the peculiar motion related to it is not a privileged inertial frame it is just a chosen reference frame where average velocity of known objects is zero.
While there’s no asymmetry in the recessional velocities in all directions for distant objects on average; the local gravitational interaction often negates Hubble flow resulting in changes in observed recessional velocities. As our observations are limited to the observable universe we have nothing to actually establish any overall velocity except for our reference frame or one we choose arbitrarily.
The apparent “velocity” from the expansion of spacetime and an increasing causal distance isn’t really movement but just an increased causal distance. The velocity dispersion of galaxies our groups is variable and depends on many factors. But it is very important to realize that velocity dispersion is the mean velocities and while in the larger scheme of things is remarkably consistent it becomes problematic with saying it is a privileged frame.
No Lorentz violations have been measured thus far and there are no known privileged frames as of this date. No frame of reference is privileged in relation to all other frames but the local reference frame is preferred. Basically this means within the local reference frame the math is easier.
If a privileged frame is found it will actually falsify several current well tested theories.
Just to throw in a tangent, consider a spinning top in space. It still experiences centripetal force even if we have no other objects to measure its speed against.
The only important speed in space is relative – not to Einstein’s relativity, but to the other object in space where you are or where you are going.
For example, in docking with the International Space Station, the important speed is that you are going 5 mi/hr faster than the ISS, and you need to get that down to near-zero to dock rather than ‘collide’. The fact that both of you are orbiting around the earth at 17,000+ mi/hr is not very relevant.
If you are going to the moon, it’s your speed toward the moon, & the distance there that matter. Yhe fact that both of you, and the whole solar system is rotating at incomprehensible speed around the galactic center is not relevant.
It’s been quite some time since I took relativity, but I do believe you cannot use something traveling at the speed of light relative to something else as a proper reference frame. So the question of how fast one photon “sees” another moving is an invalid question.
Photons don’t experience time, there is no way to define “speed” without time.
The speed of light is really the speed of causality, so you could calculate the causal connectivity etc…
It’s all very complicated :eek:
So Voyager’s speed is determined by “The dopplershift of the radio signals it transmits” or "speed relative to the “fixed stars,”
So while Voyager is hurtling away through space, the Earth is orbiting the Sun at 107000Kph or thereabouts and will sometimes be travelling in the same direction as Voyager and sometimes away from Voyager, therefore giving two different readings of Voyager speed relative to the Earth?
Another point with expanding Universe. Presumably the Big Bang worked like any explosion on Earth and flung bits of future Planets in all directions. So all the bits moving in one direction have a speed relative to the point of the Big Bang another speed relative to each other and yet another speed to bits of future planets going in the opposite direction?
Slight deviation, do we know exactly where the Big Bang happened and what is there now?
A lot of stuff to get my head round. 