\[\begin{aligned}
r_p &= a(1-e) \\
r_a &= a(1+e)
\end{aligned}\]
Variables
rpperiapsis distance (m)
raapoapsis distance (m)
asemi-major axis (m)
eorbital eccentricity
Description
What is this formula?
These formulas calculate the closest and farthest distances of an orbiting body from the focus of an elliptical orbit. The periapsis is the minimum distance, while the apoapsis is the maximum distance.
When to use it
Use these formulas when the semi-major axis and orbital eccentricity are known and the extreme orbital distances need to be determined.
Example
A satellite has:
a=12000 km
e=0.25
Formulas:
rp=a*(1-e)
ra=a*(1+e)
Substitution:
rp=12000*(1-0.25)=9000 km
ra=12000*(1+0.25)=15000 km
Result:
Periapsis distance = 9000 km
Apoapsis distance = 15000 km
Applications
- Satellite orbit analysis
- Planetary motion studies
- Space mission trajectory design
- Celestial mechanics
- Elliptical orbit characterization