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Mathematics
Differential Equations
Solving Kepler's 1st law as a function of time
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[QUOTE="jebez, post: 6819779, member: 730494"] [B]TL;DR Summary:[/B] p , ε , c constants : θ'(t)(p/(1+ε cos(θ(t))))^2=c θ(t)=? Hi I posted this differential equation to WolframAlpha [URL='https://www.wolframalpha.com/input?i2d=true&i=Power%5B%5C%2840%29Divide%5Ba%2C1%2Bb*cos%5C%2840%29y%5C%2840%29x%5C%2841%29%5C%2841%29%5D%5C%2841%29%2C2%5D*y%27%5C%2840%29x%5C%2841%29%3Dc']https://www.wolframalpha.com/input?i2d=true&i=Power[\(40)Divide[a,1+b*cos\(40)y\(40)x\(41)\(41)]\(41),2]*y'\(40)x\(41)=c[/URL] but no solution , " Standard computation time exceeded... Try again with Pro computation time " Should I ( buy and ) post to Wolfram|Alpha Pro ? I don't want to buy Pro if it doesn't solve it ... Maybe someone who has Pro can post it ? Lend his/her account ? In fact we have r(θ) = p/(1+ε cos(θ)) ( 1st Kepler's law ) , r²θ'(t)=c ( 2nd Kepler's law ) and I want r(t) so need to solve the differential equation . [URL='https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion']https://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion[/URL] Thanks . [/QUOTE]
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Solving Kepler's 1st law as a function of time
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