Hello, I'm wondering if anyone can tell me where these formulas for RA and RP (apoapsis and periapsis) come from.(adsbygoogle = window.adsbygoogle || []).push({});

RA = [itex]\frac{a(1-e^{2})}{(1-e^{2}sin^{2}(LatB))^{3/2}}[/itex]

RP = [itex]\frac{a}{(1-e^{2}sin^{2}(LatB))^{1/2}}[/itex]

If you multiply RA by [itex]\frac{1-e^{2}sin^{2}(LatB)}{1-e^{2}}[/itex], you can get RP. Seems to be a clue, but I cant figure it out.

I am trying to go from Latitude/Longitude to XYZ co-ordinates with A as the origin somewhere on the Earth, and B as the point I want to place with respect to A. Right now I am using an Excell spreadsheet which has these formulas. The spreadsheet uses the WGS84 Earth model for a,b and e.

a = semi-major axis

b = semi-minor axis

e = ellipsoid eccentricity

LatB is the latitude of the second point

I found these two on the internet, but I dont get how they relate to the other two.

RA = a(1+e)

RP = a(1-e)

It then does

R = [itex]\sqrt[]{RA\times RP}[/itex]

which is the geometric mean to find a spherical model radius for the AB area.

Any help is appreciated. Thank you.

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# Deriving Apoapsis and periapsis formulas

Can you offer guidance or do you also need help?

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