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I am trying to calculate the apogee and perigee using the orbital elements. I am checking my results against CALSPHERE 1 (https://www.n2yo.com/satellite/?s=900).

I am getting 7363599.5m as the semi major axis (a), but for the apogee and perigee, I am getting 7382482.0m and 7344717.0m respectively. I am using e as I am using the formulas: perigee = (1 - e)a apogee = (1 + e)a

I am totally confused how the major axis (semi major axis * 2.0) can be larger than the total of minimum distance and max distance from the earth? Am I crucially misunderstanding this?

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    $\begingroup$ On the linked page, the apogee and perigee numbers don't include the radius of the Earth (they are measured from some theoretical Earth surface). They are altitudes. The semi-major axis does include the radius of the Earth. Therefore, on that page, the semi-major axis is also larger than the sum of the two altitudes. Perhaps your numbers follow the same logic. $\endgroup$ Oct 26, 2022 at 21:48
  • $\begingroup$ It's not clear to me what you're confused by, except that you've misstated that the major axis is the semi-major axis * 0.5. It's the other way around; the major axis is 2*a. Your perigee, apogee, and semi-major axis all seem to check out. $\endgroup$
    – Erin Anne
    Oct 26, 2022 at 22:48
  • $\begingroup$ @OrganicMarble Thank you that's exactly it. I didn't realise they see it as from the surface. $\endgroup$
    – Ally
    Oct 26, 2022 at 22:56
  • $\begingroup$ @ErinAnne Oops, I did write that, got muddled! The question was answered by Organic, the linked page seems subtract radius of earth $\endgroup$
    – Ally
    Oct 26, 2022 at 22:58
  • $\begingroup$ Cool. Welcome to Space SE! $\endgroup$
    – Erin Anne
    Oct 26, 2022 at 23:04

1 Answer 1

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On the linked page, the apogee and perigee numbers don't include the radius of the Earth (they are measured from some theoretical Earth surface). They are altitudes. The semi-major axis does include the radius of the Earth.

This is the reason for the apparent discrepancy.

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