# Question on relative motion

• I
TL;DR Summary
Let's say your on a planet thats in a galaxy flying through space at 99.9% c. To you, you perceive you are at rest. Now let's say you point in the direction of the galaxy's motion and blast off in a rocket, and try to accelerate to 99.99% c within your frame. If your planet is already flying through space at 99.9% c unbeknownst to you, how can you accelerate at all?
its a short question...

Gold Member
Let's break this down a bit.
Summary:: Let's say your on a planet that's in a galaxy flying through space at 99.9% c.
You cannot say the galaxy "A" is flying through space at any speed, let alone, 99.9%c.
Velocity is relative. Best you can say it that galaxy A is moving relative to some other coordinate (such as another galaxy, B).
As far as galaxy A, is concerned, it - and everything in it - is stationary, and galaxy B is moving relative to it at 99.9% c.

To you, you perceive you are at rest.
You can choose whatever frame of reference you wish. If you decide to choose galaxy A as you FoR, then yes, you are at rest.

There is no such thing as objectively at rest.

Now let's say you point in the direction of the galaxy's motion and blast off in a rocket, and try to accelerate to 99.99% c within your frame.
No problem. You started at rest, so now your spaceship is moving away from galaxy A at 99.9%c.

If your planet is already flying through space at 99.9% c unbeknownst to you, how can you accelerate at all?
Here is the tricky bit: the question you want to ask is: how fast is the rocket moving away relative to galaxy B (which sees galaxy A receding at 99.9% c away from it)?

You do not add velocities simplistically in relativity. You do not simply add .999c and .999c together.

This is the formula for relativistic velocity addition:

If you set
v=0.999c and u'=0.999c
u will be 0.999999499
No matter how close your numbers are to c, the result will always be less than c.
(Try it!)

0.999999499c is how fast the rocket - leaving galaxy A - will be observed to be moving - from the frame of reference of galaxy B.

Digest that a bit, and we can get into specifics.

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Awesome thank you for answering this. Ok I think I understand. Let me see if I have this right.
So from a person on the planet in galaxy A at the spaceport watching the rocket blast off, he will see the rocket accelerate away from the planet starting at 0mph and accelerate normally up to .99%c. For the person in the rocket, he will see the same, though galaxy b appears to be traveling in the opposite direction past his solar system at .99% c and as he accelerates the galaxy keeps pushing towards the absolute limit close to 100%c.

For the person in galaxy b, he sees the planet in galaxy a flying by at .99%c. The clocks on galaxy a appear to tick nearly infinitely slowly, so even though the person in the rocket sees his speed change from 0mph to .99%c, galaxy h sees him and that change in velocity is so small because time and space are slowed and compresed relative to galaxy b...i think that's right right?
The confusing part is that person a appears to see a delta in V of ~400k mp/s, and person b sees the delta v as .00000001%c. But I guess its the per second part time dilation that preserves both perspectives reality...

DaveC426913
Gold Member
Yep. You pretty much got it.

BTW, be careful with your numbers.
.99%c is less than one per cent of c.

You want either 99%c or .99c, not both. (Convention prefers the latter.)

Homework Helper
Gold Member
2022 Award
Awesome thank you for answering this. Ok I think I understand. Let me see if I have this right.
So from a person on the planet in galaxy A at the spaceport watching the rocket blast off, he will see the rocket accelerate away from the planet starting at 0mph and accelerate normally up to .99%c. For the person in the rocket, he will see the same, though galaxy b appears to be traveling in the opposite direction past his solar system at .99% c and as he accelerates the galaxy keeps pushing towards the absolute limit close to 100%c.

For the person in galaxy b, he sees the planet in galaxy a flying by at .99%c. The clocks on galaxy a appear to tick nearly infinitely slowly, so even though the person in the rocket sees his speed change from 0mph to .99%c, galaxy h sees him and that change in velocity is so small because time and space are slowed and compresed relative to galaxy b...i think that's right right?
The confusing part is that person a appears to see a delta in V of ~400k mp/s, and person b sees the delta v as .00000001%c. But I guess its the per second part time dilation that preserves both perspectives reality...

Even more fundamentally all motion is relative. So, when you say a galaxy traveling at ##0.99c## that is only a meaningful velocity relative to something else. There's no sense in which anything is absolutely moving.

Whetever you do in a galaxy traveling at ##0.99c## (relative to some reference frame) is precisely the same as you do in a galaxy "at rest" (relative to some reference frame).

Well that's embarrassing yes thank you for pointing that out I did indeed mean .99c. Ok awesome I think I've got the idea. Its certainly not the most intuitive thing..but its clicking. Although this reminds me of something interesting I read which I vaguely remember, which Ill pose a final question regarding.

I understand and have to remind myself that when speaking of inertial reference frames, all motion is relative, and I think I've got the main concepts with respect to standard motion.
As a thought experiment take a merry go round floating in space and let's say that merry go round is rotating at a constant speed. Now if we imagine that every other particle in the universe ceases to exist leaving just the vacuum and the merry go round, where is the centrifugal force coming from? With nothing to be rotating relative to, in its own frame it should be at rest yet there will still be a force pushing away from its center right?

Gold Member
Now if we imagine that every other particle in the universe ceases to exist leaving just the vacuum and the merry go round, where is the centrifugal force coming from? With nothing to be rotating relative to, in its own frame it should be at rest yet there will still be a force pushing away from its center right?
Rotational motion is not relative.

Gold Member
Rotational motion is not relative.
So angular velocity of, say, a point on a rotating disk is independent of reference frame? I ask because it seems counterintuitive to me since in an instantaneous moment, doesn't the point have a particular linear velocity? And if so, I would assume that means that the Lorentz transformation should apply to it.

Gold Member
...doesn't the point have a particular linear velocity? And if so, I would assume that means that the Lorentz transformation should apply to it.
But the velocity is continuously changing. The Lorentz transformation is valid only for constant velocity between two inertial frames. A rotating frame isn't inertial.

Mentor
if we imagine that every other particle in the universe ceases to exist leaving just the vacuum and the merry go round, where is the centrifugal force coming from?

From the geometry of spacetime. That is what determines which states of motion are inertial (feel no force) and which are not.

Gold Member
For the person in galaxy b, he sees the planet in galaxy a flying by at .99%c. The clocks on galaxy a appear to tick nearly infinitely slowly
A clock moving at .99c ticks at about 1/7th normal rate, which is not yet "nearly infinitely slowly", but getting there...

Mentor
So angular velocity of, say, a point on a rotating disk is independent of reference frame?
It’s not rotation that is frame-independent, it’s proper acceleration (the kind that’s measured with an accelerometer). Take a box, put a weight in it, connect the weight to all six inside faces with six stretched springs so that the weight is suspended in the center of the box, and you have a simple accelerometer: when you accelerate the box by applying a force to it, the springs will stretch allowing you to measure the acceleration without reference to any external object.
It may seem a bit strange that velocity is relative but acceleration is not... bit that’s how our universe works, and it really doesn’t care whether we think it’s strange or not.

Rotational movement involves acceleration (anywhere off the axis there’s centripetal force at work to pull things onto a circular path instead of the straight line that Newton’s first law says they’d follow in the absence of any force) and our ideal accelerometer will detect that acceleration when you set down at any point on the rotating disk.