The Orbit Of Pluto

Aug 2019
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Hi all



I need help with a physics question that has stumped me and I would really love to understand the problem and be able to do it but I'm getting nowhere. I have to reproduce the answers to the question below in Mathematica which is not my problem. My problem is I do not know how to get the starting equations I need or how to derive them and Ive written down everything but nothing has worked. Any help will be greatly appreciated.


Question:



The planets move in elliptical orbits with the sun at one of the focus points of the ellipse. Pluto, while no longer officially a planet, also follows such an orbit. Here you will need to set up and solve Pluto's equation of motion in order to study its orbit. To measure time, length and mass we will use years (yr), astronomical units (AU) and solar masses M respectively. One astronomical unit is the average distance from the earth to the sun. In these units Newton's constant G has a value of 4\[Pi]^2.

At its perihelion (closest point to the sun) Pluto is a distance of 29.658 AU from the sun, and it is moving at a speed of approximately 1.287 AU/yr. Pluto's mass is 6.58x10^-9 M.

Set up and solve Pluto's equation of motion with the appropriate initial conditions. Produce a plot as well as an animation of its orbit. First write down the equation of motion (i.e. Newton's second law as a differential equation), on paper and in vector form.
 
Oct 2017
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255
Glasgow
My problem is I do not know how to get the starting equations I need or how to derive them and Ive written down everything but nothing has worked. Any help will be greatly appreciated.
If you know Newton's laws of motion and Newton's law of gravitation, that should be enough to create a model where you can calculate the orbit of a planet around the Sun as a function of time (along with some boundary conditions). However, it might also be helpful to look at Kepler's laws (which are more like the consequences of gravitation). There's also pages on the web that describe in detail the mechanics of orbits, but it can get awfully complicated very quickly, so be careful not to get too bogged down with unnecessary details.
 
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