Proof to Kepler's first and second laws

[Shahar]

I am a 10th grade student, and I tried for a few weeks now to find a proof to Kepler first and second laws.
Is there a simple proof to Kepler' s laws?

 

[Orodruin]

As with most things, this depends on your definition of "simple". You can do it pretty simple in Lagrange mechanics, but this is quite far from the scope of your typical 10th grade class. The easiest one is probably the second law, which essentially is just the conservation of angular momentum.

 

[SteamKing]

I am a 10th grade student, and I tried for a few weeks now to find a proof to Kepler first and second laws.
Is there a simple proof to Kepler' s laws?

It depends on what you consider to be "simple".

Kepler derived his three laws from examining astronomical observations made by Tycho Brahe. It took many years of work for Kepler to deduce his laws, but an explanation of why these laws were true had to wait until Isaac Newton came along. He gave an explanation in his Principia which was based on geometric principles. Other derivations involving vector calculus have been offered.

 

[Shahar]

As with most things, this depends on your definition of "simple". You can do it pretty simple in Lagrange mechanics, but this is quite far from the scope of your typical 10th grade class. The easiest one is probably the second law, which essentially is just the conservation of angular momentum.

Oh yeah, I found a solution using conversation of angular momentum.

Well I understand basic calculus(derivatives, basic integrations).