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How is the semi-major axis found if perihelion and aphelion distance are known?

For example, if an asteroid has a perihelion distance of 2.0 and an aphelion distance of 4.0 AU, what is the semi-major axis?

Answer 1

The semi major axis distance is half the sum of the perihelion and aphelion distances.

Given that the orbit is an ellipse with semi major axis a and eccentricity e, then the aphelion distance is #a(1-e)# and the aphelion distance is #a(1+e)#. Adding the two together gives #2a#. Therefor the semi major axis distance is half the sum of the perihelion and aphelion distances.

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Answer 2

Hailey Alvarez

Finding the average of the perihelion and aphelion distances will yield the semi-major axis.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.