# Fermilab

## Inquiring Minds

Centripedal Forces Plus Relativity

You wrote:
Hello,

I'm not sure if this address is the right one to write to asking a physics question. But I saw a list of questions and answers at the page with this address. Therefore, I would be very grateful if you could forward this question to someone who answers it.

Question:
I have some problems understanding centripetal and centrifugal force. As I see it, these are a result of a type of acceleration. I'm quite sure, in space these forces also "work". But I'm wondering how you measure the rotation of something. I mean, it seems, you have to define a system. And the rotation of the thing is measured comparing to this system. But now you could also say that this system was rotating compared to the thing and therefore it also had to feel a centripetal of -fugal force. So, if space was made out of two things (and there was nothing else) and they would rotate compared to each other would then their mass and distance influence the size of the centripetal forces the two things feel?

Another question, that I think is related to the first one: How is fastness and acceleration measured in the theory of relativity. As far as I know it says, nothing can travel faster than light. But does this mean, the distance of any two things can't increase or decrease faster than with speed of light? Thanks for answering,

Dave

Dear Dave:

I'm glad to see that we get questions from Switzerland. Thank you very much for your interest.

If space contained only two things and they would rotate compared to each other, would their mass and distance influence the size of the centripetal forces the two things feel?

Yes. Think of the universe being completely empty except for earth and moon. For someone sitting on the earth (and who knows about gravitational forces), it seems as if there is a force that is making sure that the moon is staying up in the sky, counterbalancing the gravitational pull toward earth. The heavier the moon, the bigger the force to keep it up there.

For someone looking at the situation from a spaceship, it is clear what really causes the force that prevents the moon from crashing into earth: the rotation. Earth and moon rotate around each other like two spinning ice-skaters, but they don't need to hold hands as they have enough gravitational attraction. (Perhaps think of it as an invisible rubber band.) The person looking on from the outside clearly identifies the centrifugal force as the force to keep the moon from approaching earth.

In general relativity, can the distance of any two things increase or decrease faster than the speed of light?

Great question. In general, nothing can travel faster than the speed of light. Think of space as an invisible carpet, and you are running across this carpet. Since you have a mass, you will always move slower than the speed of light, no matter how much energy is available for you to accelerate. (Only massless objects can move at the speed of light.)

When our universe was "born" in a Big Bang, something remarkable seems to have happened (at least to our current theory and present experimental observations in astrophysics). Space itself expanded. Physicists call this phase after the Big Bang the period of inflation. Think of it as if the invisible carpet is being stretched and getting longer. Well, there is no speed limit on this expansion of space. And space expanded very fast at early times. Even you and I, just "walking on this invisible carpet," would have been faster than the speed of light.

Astrophysicists have actually made a recent discovery that confirms the inflation theory. Check out the explanation at http://www.sdss.org/news/releases/20000413.qso.q.html

The discovery of the most distant quasar is described at http://www.sdss.org/news/releases/20000413.qso.html

Best wishes,

Kurt Riesselmann Fermilab

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