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This is not a homework or coursework question (if it were it would be of the project type), and I am looking for hints not spoilers.

Hi,

I recently passed by kepler's laws again in a science class (this time earth science), and am concurrently taking calculus in my math class.

I realized that my current knowledge of calculus should let me be able to re-find kepler's laws (or show equivalence to newton's laws) - for kepler's first law, I should be able to prove (with newton's second law) that the elliptical orbit described is consistent. For his second law, I should be able to use polar integration to complete the consistency proof. As for the third, I haven't had any ideas, but my problems are really with where to start.

1. The problem statement, all variables and given/known data

I contacted my math teacher with this question, and we had a short discussion, with my teacher suggesting I get data of planetary locations over time. I searched for these, with no avail (I am not looking for conclusions - which are all I could seemingly find). I'm trying to understand kepler's first law and how it relates to newton's laws - but I do realize some problems. Since initial velocity (and position) must be known in order to determine the elliptical path, one must have these accounted for - and I have no idea how to do that.

I need hints, and if possible, data.

I do not want a result, or work and a result, because I want to in a sense "repioneer" this - the thinking that is involved with creating an idea previously unknown to one differs from that of learning about an idea.

tl;dr:I am trying to reconstruct Newton's derivation of Kepler's laws, and am stuck on how to translate newton's laws into kepler's first law. I need hints, and if possible, data.

2. Relevant equations

newton's second law: f=ma

newton's gravitational law:f=g(m_1m_2)/(r^2)

kepler's 3 laws

3. The attempt at a solution

I'm not sure where to start.

I know that once I get an idea I will break motion into x and y axis (put in parametric form), and try to convert to polar form as well. I am guessing I will encounter simple differential equations.

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# Newton's derivation of Kepler's laws

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