# How much does relativity effect matter?

1. Aug 6, 2014

### thefredman

Hi everyone,

I have a few questions about relativity.

I've been reading about relativity and its effects and I began to wonder at what point does it become a variable worth mentioning?

Suppose there were 3 solar systems each with an earth that revolved around the sun. Earth 1 does not revolve around the sun. Earth 2 revolves around the sun at 50% the speed of light. Earth 3 revolves around the sun at 100% the speed of light or near. Suppose each earth was populated at the same time. Would the people on the different earths age differently?

If there is a difference does that mean that other planets in our solar system actually have matter that is millions or years older or younger than the same matter here on earth? For instance, the surface of mars could be millions of years younger than the surface of earth because it travels through space at a different speed.

What would happen if you extrapolate time to other star systems?

I have about 100 other questions but I'll leave it at that.

Thanks,

2. Aug 6, 2014

### Chronos

An earth orbiting at near light speed would be VERY close to its mother star - as in deep fried to a crispy critter close. Planets simply do not orbit at anywhere near relativistic speeds. Try calculating the distance a planet would have to be from a black hole to orbit at .5c.

3. Aug 6, 2014

### Staff: Mentor

Most relativistic effects are proportional to the quantity
$$\gamma = \frac{1}{\sqrt{1-v^2/c^2}}$$
so you can calculate that and see whether the relativistic effects are large enough to care about. If it comes out 1.01, then your error from ignoring relativity will be 1%; if it comes out 1.10 your error will be 10%; if it comes out 42 the then your error will be 4200%.
(Sanity check: set $v=0$ and $\gamma$ comes out to exactly one, meaning no error from ignoring relativity when there is no relative motion)

4. Aug 6, 2014

### thefredman

I guess I should have stated that I'm not a physicist and those calculations are over my head.

My question is more geared towards a hypothetical situation. In a system where there are multiple earths traveling through space-time at different speeds what would the effect of relativity be?

Thank you for your answer though. Is it right to infer in a "real-life" scenario the differences in distance from a host star the speed from which the planet travels through space conserves time? For instance, if 3 earths in the same solar system traveling at different speeds would have the same concept of time because of their distance from each other in space time.

5. Aug 7, 2014

### phinds

In the real world ... essentially none. Chronos already answered this by correctly stating "Planets simply do not orbit at anywhere near relativistic speeds"

I have no idea what you are asking here. What do you mean by "conserving time" ?

6. Aug 7, 2014

### thefredman

At what point does speed become relativistic? Is there a threshold that says any object that travels under this speed is not subject to relativity? Considering the age of the universe doesn't any speed become, at some point, relativistic? Even astronauts on the ISS are subject to the effects relativity and they are not traveling at astronomical speeds.

Suppose two objects, the earth and the ISS, begin orbiting the sun at the same time. Over the course of 4.5 billion years would it be correct to assume there would be a considerable difference in time between the ISS and the earth?

I have no idea what you are asking here. What do you mean by "conserving time" ?

I guess the best way I can put it right now would be if you had one planet traveling at high speeds around the sun and a planet traveling much further away at a much slower speed essentially time would remain reserved because the distance.

7. Aug 7, 2014

### phinds

No, relativity is a description of reality. Period. The EFFECTS of relativity are vanishingly small at low speeds in a frame of reference and at low gravity.

You are assuming, I think, that there is some absolute speed. There is no such thing. You, right now as you read this, are travelling at .999999c relative to a particle at CERN and you are traveling at zero in your own frame of reference.

Assuming you mean the ISS is orbiting the Earth then the fact that they are both orbiting the sun is irrelevant. Yes there would be a difference. How much would depend on how long and what the orbit is.

I don't know what you mean by "time would remain reversed". Relative to what?

8. Aug 7, 2014

### Staff: Mentor

There is no such threshold. Everything is always subject to relativity, it's just that sometimes (nearly always in day to day life) the effects are small enough that we ignore them instead of going to the trouble of calculating them.

For example: A small passenger jet will burn 25 kilograms of fuel per minute at cruise. How much fuel must the plane carry for a one-hour flight? Ignoring relativity, the answer is easy: 25 kilograms per minute times 60 minutes means 1500 kilograms. Include the effects of relativity, and the answer will be something like 1500.0000000... kilograms, with the first non-zero digit showing up around the tenth decimal place. The amount of dust on a passenger's shoes would make a much bigger difference.

We also don't worry about the effects of relativity when we're calculating satellite orbits... but we do when operating a GPS system. It all depends on the accuracy you need.

Last edited: Aug 7, 2014
9. Aug 7, 2014

### thefredman

Over the course of 4.5 billion years would the difference be noticeable, like millions of years? Would the same rule apply to other planets in our solar system such as the moon or mars? Are rocks on other planets millions of years older or younger? Or are the effects of relativity not really noticeable even though they accrued over such long periods of time (4.5 billion years)?

I would imagine it could be useful to view the ionization of atoms from matter millions of years in the future or the past.

Relative to the gravitational constant as dictated by the sun since they share the same field of gravity.

10. Aug 7, 2014

### HallsofIvy

Staff Emeritus
"time" is NOT "relative to the gravitational constant" so we still don't know what you mean by that.

11. Aug 8, 2014

### thefredman

Suppose there is one planetary body and 2 orbit objects. Object 1 orbits the planet at near escape velocity while object 2 orbits much further away at near the escape velocity at that distance. While both objects are moving relative to the planet they each share the same time frame of reference because the distance between them. Or the distance and the speed that they travel at are proportional to the observer, in this case the planet. Therefore time is conserved because the laws of gravity won't allow one to be no longer relative to the other.

12. Aug 15, 2014

### Barry911

GR contains the two tensor functions (Ricci -Weyl both can be obtained from the Riemann space).
The Ricci tensor represents the volume reducing component of a mass under gravitation. Importantly
it creates an energy-density gradient from surface to core. The core temperature and density can ,with
sufficient mass lead to fusion. The Weyl tensor describes the effect of gravity outside (but in the
vicinity) of the gravitating mass. The tidal force is primarily a Ricci consequence but the additional
Weyl component preserves a rather beautiful symmetry....it conserves the elliptical volume

Respectfully

Barry