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? asked in Science & MathematicsMathematics · 8 years ago

Calculus 2 Kepler Law finding Minor axis?

A comet has an elliptical orbit with the sun at one focus and has an eccentricity of e ≈ 0.928. The length of the major axis of the orbit is approximately 620 astronomical units. The minimum distance (perihelion) from the sun to the comet is

r = a(1 − e)

and the maximum distance (aphelion) is

r = a(1 + e).

1) Length of its Minor axis = ????

Thanks in advance!

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  • 8 years ago
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    length of major axis

    r = a(1 + e)

    L = 2r

    L = a(1 + 0.928)

    L = 1.928a

    620 = 1.928a

    a = 620/1.928

    length of minor axis

    L = 2r

    L = 2a(1 - e)

    L = 2(620/1.928)(1 - 0.928)

    L = 46.3 astronomical units

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