# List of different relative speeds?

#### JT73

Hello,

Let me first say this is not homework, If you do not beleive me you can use any numbers you would like. I am just curious and would like to see how the "speed" of an object changes relative to different things.

Basically, if say, I move 10 mph (or 20 mph, or 5 feet a second, it doesn't matter) here on earth what would that speed be relative to other objects in the universe? Such as a frame of reference from a space station, or from jupiter, or from another galaxy, etc...

Thanks

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#### ghwellsjr

Science Advisor
Gold Member
Relative speeds between two objects are the same when viewed from the other object but you have to take into account both objects and not include a third object. So if you say you are going 10 mph on the earth and the space station is going 18,000 mph relative to the earth, there is not enough information to say how fast the space station is going relative to you or vice versa because you haven't told us the directions you are each going.

A better way to think about it is two objects in space traveling in straight lines at constant velocities (no changing speed or direction). Then you can say whatever speed object A is traveling with respect to object B is the same speed that object B is traveling with respect to object A.

If you want to include more objects, then it gets rather complicated unless they are all traveling along the same straight line. Then you can use the "velocity addition" formula (look it up in wikipedia) to see how fast A is traveling relative to B when you know how fast A and B are traveling relative to C.

#### JT73

Oh alright, yeah I meant that both myself and the space station are traveling in the same direction on a straigh line. I'll look up the velocity addition formula thanks

#### DNMock

Should just be simple addition.

Two people are playing catch on a train that is going 75 km/h.

The two people on the train see the ball as going 50 km/h, so relative to the two people on the train, the ball is going 50 km/h.

To a viewer on the ground, the ball is going 125 km/h. The same works in reverse, The ball will see the person who threw it moving away at 50 km/h, and will see the person on the ground, outside the train going away at 125 km/h since the train itself is moving 75 km/h.

Simply put, in a straight line, convert to the same units of measure and add em.

#### Naty1

Should just be simple addition.
That works for approximations at low relative speeds...where space and time remain about constant......but Einstein's special relativity theory shows that at speeds which are a significant fraction of light (c), a different formula is required for accurate calculations.

You can read about it here:

http://en.wikipedia.org/wiki/Special_relativity

#### DNMock

That works for approximations at low relative speeds...where space and time remain about constant......but Einstein's special relativity theory shows that at speeds which are a significant fraction of light (c), a different formula is required for accurate calculations.

You can read about it here:

http://en.wikipedia.org/wiki/Special_relativity
Yeah, seemed that since the OP was only wanting stuff in a basic form since he was wanting it all in a perfectly straight vector, hence why I went with the newton style rather than the GR/SR versions.

#### JT73

Hmm okay this makes sense, I was just curious if there was some type of list someone made relating different speeds(in a straight line in the same direction), both relatively slow and that of a significant fraction of the speed of light to the object doing the movement and an observer. I think a list like that would be cool.

Science Advisor
Gold Member

#### JT73

Ugh, no not really. I'm getting frustrated with myself because my ignorance of the subject is shining through (but im trying to learn!).

From my understanding If i am, whereever I am (it doesn't matter), then to myself I travel a certain speed relative to whatever I am relating it to. Now from another person's view at a different position it may seem like I am not traveling at the speed that I recorded.

So, as in my OP, If I am traveling 10 mph on earth and another observer on earth next to me notes that I am traveling 10 mph, what would someone from a different reference point see me traveling at the speed of? And then again what would another person from yet another far out distant point see me traveling at. (Obviously these people have the ability to see me somehow)

#### JT73

I think I just realized how to word this. It is said that the speed of light is always recorded to be C no matter from what reference frame.

So for things moving not at C, is there a list of how fast these objects seem to be moving from multiple different reference frames?

#### ghwellsjr

Science Advisor
Gold Member
It seems my first answer from post #2 is what you are looking for. We could make a table like an addition table that shows a list of speeds going down and another list of speeds going across which would be the results of applying the "velocity addition" formula that is in the wikipedia article. It would be for a "stationary" observer looking at two other observers moving either in the same direction or in the opposite direction. You look up the speeds of the two observers and where the row and column intersect, you find the speed that they are going relative to each other. Is that what you are looking for?

#### ghwellsjr

Science Advisor
Gold Member
I'm going to assume that is what you want. Here's a table for the two observers traveling in the opposite direction:
Code:
   0.000   0.100   0.200   0.300   0.400   0.500   0.600   0.700   0.800   0.900
0.100   0.198   0.294   0.388   0.481   0.571   0.660   0.748   0.833   0.917
0.200   0.294   0.385   0.472   0.556   0.636   0.714   0.789   0.862   0.932
0.300   0.388   0.472   0.550   0.625   0.696   0.763   0.826   0.887   0.945
0.400   0.481   0.556   0.625   0.690   0.750   0.806   0.859   0.909   0.956
0.500   0.571   0.636   0.696   0.750   0.800   0.846   0.889   0.929   0.966
0.600   0.660   0.714   0.763   0.806   0.846   0.882   0.915   0.946   0.974
0.700   0.748   0.789   0.826   0.859   0.889   0.915   0.940   0.962   0.982
0.800   0.833   0.862   0.887   0.909   0.929   0.946   0.962   0.976   0.988
0.900   0.917   0.932   0.945   0.956   0.966   0.974   0.982   0.988   0.994
And here's one for when they're traveling in the same direction:
Code:
   0.000   0.100   0.200   0.300   0.400   0.500   0.600   0.700   0.800   0.900
0.100   0.000   0.102   0.206   0.313   0.421   0.532   0.645   0.761   0.879
0.200   0.102   0.000   0.106   0.217   0.333   0.455   0.581   0.714   0.854
0.300   0.206   0.106   0.000   0.114   0.235   0.366   0.506   0.658   0.822
0.400   0.313   0.217   0.114   0.000   0.125   0.263   0.417   0.588   0.781
0.500   0.421   0.333   0.235   0.125   0.000   0.143   0.308   0.500   0.727
0.600   0.532   0.455   0.366   0.263   0.143   0.000   0.172   0.385   0.652
0.700   0.645   0.581   0.506   0.417   0.308   0.172   0.000   0.227   0.541
0.800   0.761   0.714   0.658   0.588   0.500   0.385   0.227   0.000   0.357
0.900   0.879   0.854   0.822   0.781   0.727   0.652   0.541   0.357   0.000
The numbers are in fractions of the speed of light. So, for example if the one traveler is going at 0.4c in one direction and the other one is going 0.8c in the other direction, you use the first table and see that they are going 0.909c apart from each other. Or if they are going those same two speeds in the same direction, you use the second table and see that they are going 0.588c apart from each other.

#### JT73

Hm not quite what I was talking about, but thats because of my lack of being able to describe my thoughts, nothing on your part.

This table is however something else that Is Definately useful/interesting.

Thanks for not being a dick at all throughout this thread, man. Some users on here, whether they try to it, just come across dick-ish. Theyre probably just used to a lot of wrong informationm being spread though.

#### ghwellsjr

Science Advisor
Gold Member
Well, maybe my tables are the answer to your question but I just haven't explained how you use it in the way you want to. So let's say I'm going at 0.1c relative to earth so you could say in the earth frame I'm traveling at 0.1c. Now if you want to know how fast I appear to someone else traveling at another speed relative to earth (or you could say in a different frame relative to earth) at, say 0.2c in the same direction that I'm traveling, will see me going 0.102c or if they were going in the opposite direction they would see me going 0.294c. It doesn't matter how far away they are from me or the earth, as long as we're all in the same line.

If that isn't what you're looking for, try to explain what I'm doing wrong and how it differs from what you want.

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