Calculate aphelion and perihelion distances
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Calculate aphelion and perihelion distances

[From: ] [author: ] [Date: 11-05-17] [Hit: ]
3/(1-0.073) = 1.......
As a planet revolves around the sun, the distance from the sun, as a function of the angular position φ, is given by the function
r(φ) = α / [ 1+ε cos(φ−φ0) ].
Calculate the perihelion and aphelion distances where we know α=1.3 ε=0.073 and φ0= 5.0

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Perihelion occurs when cos(φ−φ0) =1, this occurs when φ =5° since φ0= 5.0° and φ−φ0 =0°
Then r(φ) = α / [ 1+ε cos(φ−φ0) ] = α / [ 1+ε] = 1.3/(1 +0.073) = 1.212
Aphelion occurs when cos(φ−φ0) = -1, this occurs when 185°
Then r(φ) = α / [ 1+ε cos(φ−φ0) ] = α / [ 1-ε]= 1.3/(1-0.073) = 1.402
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keywords: Calculate,and,perihelion,distances,aphelion,Calculate aphelion and perihelion distances
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