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Question 550078: Question 550077: Please provide me with a couple of formulas to rearange:
P= (sqrt of (perihelion / (1-e))cubed)) so that I can determine
a: eccentricity
b: perihelion
I thought that I'd found out how to rearange it for perihelion, but when various values were plugged in, the results were incorrect. I'm sure that all that I missed was an operation overlooked.
The [ P ]value is "period"
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Please provide me with a couple of formulas to rearange:
P= (sqrt of (perihelion / (1-e))cubed)) so that I can determine
a: eccentricity = ?
(1-e)^3 = sqrt(peri)/P
---
Take the cube root of both sides to get:
1-e = (peri)^(1/6)/P^(1/3)
---
e = 1-[(peri)^(1/6)/P^(1/3)]
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P= (sqrt of (perihelion / (1-e))cubed))
b: perihelion = ?
sqrt(peri) = P*(1-e)^3
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square both sides to get:
peri = [P*(1-e)^3]^2
---
peri = P^2*(1-e)^6
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Cheers,
Stan H.
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