# Math Help - Path of an orbiting object

1. ## Path of an orbiting object

I am a clueless math noob, and I hope the overlords of the internet can help me explain, what I cannot.

Hopefully someone can explain, not only the formula itself, but also learn me how I can understand it.

The problem is as follows:

I want to describe the orbit of an object in a formula.
The object travels in a circular path, but is controlled by an arm, set off-center from the center of its path.

The arm rotates in a constant speed.

So my problem is, how can I describe this mathematically?

2. ## Re: Path of an orbiting object

Originally Posted by Stig
I am a clueless math noob, and I hope the overlords of the internet can help me explain, what I cannot.

Hopefully someone can explain, not only the formula itself, but also learn my how I can understand it.

The problem is as follows:

I want to describe the orbit of an object in a formula.
The object travels in a circular path, but is controlled by an arm, set off-center from the center of its path.

The arm rotates in a constant speed.

So my problem is, how can I describe this in mathematically?

If I understand your question correctly this is only possible if the length of the arm is variable.

1. The orbit is a circle with radius R (= constant). The center of rotation is in a distance d from the center of the orbit. (see attachment)

2. From the Cosine rule you know:

$R^2=d^2+r^2-2dr \cdot cos(\theta)$

This ia a quadratic equation in r. Solve for r. I've got:

$r = d \cdot \cos(\theta) \pm \sqrt{d^2 \cdot (\cos(\theta))^2 + R^2 - d^2}$

3. Use this equation together with a polar coordinate system.

4. For instance with R = 4, d = 2 you'll get a circle around (2, 0) radius 4 and the center of rotation (of the "arm") is the origin.

3. ## Re: Path of an orbiting object

Thank you so very much!
I owe you a beer

4. ## Re: Path of an orbiting object

I have another issue which I hope can be explained...
If the object has a mass, how will the forces be distributed?
Say if one kg moves at the circular path, how much outward force will be distributed in this circle?