# How fast we travel?

1. Jan 17, 2013

### cryptist

If earth is moving with the speed of 800 km/s in universe, then do we travel at 1/375 of the speed of light according to a hypothetical static point in universe?

2. Jan 17, 2013

### HallsofIvy

You posted this in "Special and General Relativity" so surely you know that speed can only be given relative to some specific point. So I have no idea where you got the figure "800 km/s in universe". You say "according to" (relative to) some "hypothetical static point" but since speed is relative there is NO independently "static" point.

3. Jan 18, 2013

### BenG549

Accepting that you might have just worded this question badly.

So the speed of an object is dependant on the reference frame i.e. Imagine that I live on the equator, me and my dad are both sitting in the living room, in this reference frame his velocity is 0. At the equator, the circumference of the Earth is 40,070 kilometers, and the day is 24 hours long (approximately) so the speed is 1670 kilometers/hour ( 1070 miles/hr), hence my dad is moving at 1670km/h, but the orbital speed of the Earth averages about 29.8 km/s (107,000 km/h), so is he not moving at 29.8 km/s. The truth is that there are reference frames in which my dad is moving 0km/s, there are reference frames in which he is moving at 30km/s and hypothetically there are reference frame in which he is moving at the speed of light.

If by hypothetical static point in the universe you mean. If the earth is moving with velocity x,are we not also moving at velocity x, then yes we are. But if you walk towards the front of a flying plane you don't say I'm walking at 570 (+ 3)mph you don't look like your walking at 573 mph to someone on the plane. Someone on the floor however will see the plane and assuming they can see you, it will look like you are travelling at the 573mph (assuming the plane is travelling at 570 mph and you walk at approximately 3mph.)

Does this make sense... does it go anyway to answering your question?

4. Jan 18, 2013

### ghwellsjr

No, hypothetically there are reference frames in which he is moving as close to the speed of light as you want, but not at the speed of light. As Einstein said, "the velocity of light in our theory plays the part, physically, of an infinitely great velocity" which means you can never reach it.

5. Jan 18, 2013

### nitsuj

Yet motion is relative and space is expanding.

6. Jan 18, 2013

### BenG549

Sorry, not a physicist; I have a conceptual knowledge of relativity and the ideas and limitations of travelling close to/at the speed of light but I was assuming that, for example if I were in a ship travelling in one direction at 0.5c, someone travelling in the opposite direction at 0.5 would appear to be travelling at the speed of light, as within my reference frame I am stationary... I take it I've made a basic error in my assumption here? Nothing is actually travelling at light speed.

Last edited: Jan 18, 2013
7. Jan 18, 2013

### Staff: Mentor

Nope, speeds don't add that way. In the situation you describe, where u is the speed of the left moving ship (as observed by an observer in the middle) and v is the speed of the right-moving ship (also as observed by an observer in the middle) the two ships will see each other approaching at a speed that is NOT u+v; it will be $$\frac{u+v}{1+\frac{uv}{c^2}}$$

The reason you've never noticed this is because c2 is a very large number, so at any of the speeds that we've ever experienced, the difference between the two formulas is not noticeable. When you're talking about things moving at an appreciable fraction of the speed of light, it starts to matter.

Last edited: Jan 18, 2013
8. Jan 18, 2013

### BenG549

Ahhh, right. Nice one, good knowledge I'll remember that! So in fact the observed speed would be: v = c/(1+0.25).... i.e. 0.8c. Cool.

I have to admit the idea of being able to observe something appearing to travel faster than light did give me pause for thought lol.

9. Jan 20, 2013

### cryptist

My question is not badly worded actually. I guess we are not talking about the same thing.

Earth is moving with a velocity, solar system is moving with a velocity, milky way is moving with a velocity. I couldn't find where I got this number but, somewhere it says earth is in total moving with a velocity 800 km/s. (If this number is wrong, please feel free to write the right one..)

Since we are on earth, we are also moving with that velocity. So if that number is right, we are actually travelling at 1/375 of the speed of light. Well, I know of course, its all relative, and that's why I called it as hypothetical static point. If it was real, I would not write hypothetical. Imagine yourself outside of our space-time. Then, you are a static point. I'm talking about that point..

10. Jan 20, 2013

### Staff: Mentor

That speed was relative to something - your source may not have said what it was (in which case they were either being very sloppy or speaking in a context in which it should have been obvious) but it was relative to something. You might have some fun with this page but please do remember that all of the speeds they mention there are relative to something.

Any conclusion we come to as a result of thinking about this hypothetical point is itself hypothetical. It's sort of as if you're asking "If hypothetically a pig had wings, I know pigs don't have wings and can't fly, but suppose they did and could, would a pig be able to fly faster than a bumblebee?".

11. Jan 20, 2013

### Naty1

We also move on the surface of the earth relative to the center of the earth.....v =wr, and we have another speed relative to, say, the center of our solar system, another relative to the center of our galaxy, and we are moving 'faster than the speed of light' relative to the observers just past the Hubble radius from us....v = HD.......

12. Jan 20, 2013

### cryptist

Actually it says "1 second after, earth will be 800km far away from this point" So I conclude that earth is moving with 800km/s, of course as you all said, relative to some reference point.

13. Jan 20, 2013

### DiracPool

Let me simplify things here because getting too fancy about this velocity versus that radius, etc. is confounding the issue. The fact is that I can say that the Earth or a clown or any other object I can imagine travels at any speed I want simply by designating a hypothetical "static" point in space that my object moves relative to. Don't bother trying to find the reference to the exact velocity that you heard the Earth moves through the universe, just make one up.

Yes. You got it! Next time give a tougher one we can actually calculate :)

14. Jan 21, 2013

### arindamsinha

I suspect you got this number from velocity w.r.t. the CMBR (Cosmic Microwave Background Radiation).

Our local group of galaxies is moving at 600 km/s w.r.t CMBR, so that is the approximate velocity of the Milky Way too. Very 'back of the envelope' calculation - add another 220 km/s as the Sun's velocity around the Milky Way center, and you get something roughly around 800 km/s.

15. Jan 23, 2013

### DiracPool

Interesting, can you provide a link for these figures? Especially the CMBR? Thanks.

16. Jan 23, 2013

### Naty1

source [60] ^ Kogut, A.; et al. (1993). "Dipole Anisotropy in the COBE Differential Microwave Radiometers First-Year Sky Maps". Astrophysical Journal 419: 1–6. arXiv:astro-ph/9312056. Bibcode 1993ApJ...419....1K. doi:10.1086/173453.

17. Jan 23, 2013

### DiracPool

Thanks Naty

18. Jan 23, 2013