Maple demonstration of kepler law

[kakolukia786]

Hello,

I have been trying to do an assignment for one of my physics class. We are trying to demonstrate the planetary motion using Kepler's law. I have been trying to solve a integral. I was able to solve it using maple. I am trying to solve equation 29 in attached figure. I got equation 31 after integration and simplification.

My question from this equation, how do I evaluate this so that I can get answer as a conic section in polar coordinates. I assume the solution I got is correct as I am getting a desired plot. Please suggest me.

Thank You

 

[mighty2000]

Hello,

Thank you for reaching out with your question. It's great to see that you are working on a physics assignment related to planetary motion and using Kepler's law. Solving integrals can be challenging, but it seems like you have made some progress already.

To evaluate equation 31 and get an answer in the form of a conic section in polar coordinates, you can use the following steps:

1. First, substitute the values of a, e, and M from equation 31 into the equation for a conic section in polar coordinates: r = (a(1-e^2))/(1+e*cos(theta))

2. Simplify the equation by multiplying both numerator and denominator by (1-e*cos(theta))

3. This should give you the equation of a conic section in polar coordinates: r = a(1-e*cos(theta))

4. Now, you can plot this equation in polar coordinates to get a graph of the conic section, which should match the desired plot you mentioned.

I hope this helps. If you have any further questions or need clarification, please don't hesitate to reach out. Good luck with your assignment!