Major axis larger than total of apogee and perigee?

Question

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?

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. — Organic Marble, Oct 26 '22 at 21:48
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. — Erin Anne, Oct 26 '22 at 22:48
@OrganicMarble Thank you that's exactly it. I didn't realise they see it as from the surface. — Ally, Oct 26 '22 at 22:56
@ErinAnne Oops, I did write that, got muddled! The question was answered by Organic, the linked page seems subtract radius of earth — Ally, Oct 26 '22 at 22:58
You may find these helpful as well: Failing at getting apogee and perigee from TLE and How is the altitude of a satellite defined, given that the Earth is not spherical? and How big is an orbit of "X by Y miles"? — uhoh, Oct 27 '22 at 10:29

score 12 · Accepted Answer · answered Oct 26 '22 at 23:09

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.

Major axis larger than total of apogee and perigee?

1 Answers1