# Relativistic Circular Motion

• quantumdude
In summary: Not sure if it would be of help. I can't help you with the question about special requirements for LT, sorry!

#### quantumdude

Staff Emeritus
Gold Member
I am working on a problem, and have gotten stuck.

Two masses orbit around a stationary attracting center with radii R1 and R2, R1<R2. They orbit in such a way that, in frame S1, the Sun, S1, and S2 are all collinear.

I am using Marzke-Wheeler coordinates for accelerated observers, detailed here:
http://xxx.lanl.gov/pdf/gr-qc/0006095

The scenario for a single frame in circular motion is described on page 19.

What I want to know is, what do I have to do to Lorentz boost among accelerating frames? Is it the old LT, or do I have to modify it for the acceleration?

Thanks,

Tom!

i don't know what you're going to think of me but i can simulate gravitational or Coulombian rotations without acceleration in the calculus.would it be of any help?

How do you simulate circular motion without rotations? Remember, this is not general relativity. Also, do you know how to address the question at hand, namely: Is there anything special I need to do to Lorentz transform between accelerated frames?

Originally posted by Tom
How do you simulate circular motion without rotations? Remember, this is not general relativity. Also, do you know how to address the question at hand, namely: Is there anything special I need to do to Lorentz transform between accelerated frames?
no.i didn't meant circular motion without rotations (it's impossible)but "simulating circular motion without acceleration in the calculus of the trajectories".i'm so anccious to start working on that simulation in delphi.i don't have the language at the moment.i'll start tommorow.i can give you a clue of what I'm thinking by writing it down in MSWord and mail it to you.by the way you could be the first to (dis)agree with it.

regarding your q since there is no need of acceleration in the calculus you don't need to do any changes to LT.just use them how they are.at least this is how i understand your q;as if you wonder wather you need to acomodate LT to support transpassing between accelerated frames.

Originally posted by Tom
How do you simulate circular motion without rotations?

Sorry, I meant "acceleration", not "rotations". You can do this in GR, because an orbit is a free-fall frame, but in SR it is still considered an acceleration.

i'll post what i have on it in the attachment.It's only classical physics but not usual classical physics but classical physics in marsian sense.

#### Attachments

• simulating circular motion without the acceleration.doc
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accelerated transformations

I think that the paper made a mess of something fairly simple. The transformations that they gave and which the paper are all about ARE the Lorentz transformations modified to describe particular states of acceleration. 1 constant proper acceleration and 2 circular motion. They are Lorentz boosts. I have transformation for arbitrarily accelerated states.
see equation 5.4.4 at-
http://www.geocities.com/zcphysicsms/chap5.htm#BM5_4
These are a Lorentz boost from an arbitrarily accelerated frame including orbital motion without "spin" to an inertial frame. At the following link there is an example on their use which is applied to an accelerated observer who orbits a center that is taken as the origin for an inertial frame. Relating two arbitrarily accelerated frame coordinate systems would be done in general by first relating each to a common inertial frame through equations 5.4.4 and then solving the systems of equations simply by first setting the right hand side of each system equal to each-other.

Whatever the source of the potential

&gamma; = (1-(dU/drc2)-1/2

learned that one from Creator.

## 1. What is relativistic circular motion?

Relativistic circular motion is a type of motion in which an object moves in a circular path at high speeds, close to the speed of light. It takes into account the effects of special relativity, such as time dilation and length contraction.

## 2. How is relativistic circular motion different from classical circular motion?

Relativistic circular motion incorporates the effects of special relativity, while classical circular motion does not. This means that in relativistic circular motion, the speed of the object is close to the speed of light, and its mass, time, and length are affected by its high speed. In classical circular motion, these effects are negligible.

## 3. What is the equation for calculating the relativistic centripetal force?

The equation for calculating the relativistic centripetal force is F = (mγv^2)/r, where m is the mass of the object, γ is the Lorentz factor (1/√(1-v^2/c^2)), v is the speed of the object, and r is the radius of the circular path.

## 4. How does relativistic circular motion affect the concept of time?

Relativistic circular motion causes time dilation, meaning that time appears to pass slower for an object moving at high speeds. This is due to the fact that the faster an object moves, the more its time appears to slow down, according to the theory of special relativity.

## 5. Can an object travel at the speed of light in relativistic circular motion?

No, according to the theory of special relativity, an object with mass cannot travel at the speed of light. As an object's speed approaches the speed of light, its mass, time, and length become infinite, making it impossible to reach the speed of light.