An elliptical orbit has a high point and a low point measured from Earth, and these points are central to astronautics. The farthest point from Earth is called apogee, and the nearest point is called perigee. These distances affect communication coverage, mission timing, fuel planning, and reentry safety.
Understanding apogee and perigee helps explain why spacecraft do not move at one constant speed around Earth.
Earth is not at the center of an elliptical orbit, but at one focus of the ellipse. A spacecraft moves fastest at perigee because Earth’s gravity has accelerated it as it falls inward, and it moves slowest at apogee because it has climbed outward against gravity. Engineers change an orbit by firing engines at carefully chosen points, often using a burn at perigee to raise apogee or a burn at apogee to change perigee.
This connection between altitude, speed, and energy is the foundation of many satellite maneuvers.
Key Facts
- Apogee is the point in an Earth orbit farthest from Earth’s center.
- Perigee is the point in an Earth orbit closest to Earth’s center.
- Orbital speed is highest at perigee and lowest at apogee.
- For an ellipse, r_p = a(1 - e) and r_a = a(1 + e), where r_p is perigee radius, r_a is apogee radius, a is semi-major axis, and e is eccentricity.
- Specific orbital energy is epsilon = v^2/2 - mu/r = -mu/(2a).
- Vis-viva equation: v = sqrt(mu(2/r - 1/a)), where mu is Earth’s gravitational parameter.
Vocabulary
- Apogee
- The point in an Earth-centered orbit where a spacecraft is farthest from Earth’s center.
- Perigee
- The point in an Earth-centered orbit where a spacecraft is closest to Earth’s center.
- Ellipse
- A stretched circular shape with two focus points, one of which is occupied by Earth in an ideal Earth orbit.
- Eccentricity
- A number that describes how stretched an orbit is, with 0 for a circle and values closer to 1 for a more elongated ellipse.
- Orbital speed
- The speed of a spacecraft as it travels along its orbit, which changes in an elliptical orbit.
Common Mistakes to Avoid
- Putting Earth at the exact center of an elliptical orbit is wrong because Earth lies at one focus, not the center of the ellipse.
- Saying the spacecraft moves fastest at apogee is wrong because orbital speed is highest at perigee, where the spacecraft is closest to Earth and has the most kinetic energy.
- Measuring apogee and perigee from Earth’s surface without saying so can be confusing because orbital formulas usually use distance from Earth’s center.
- Assuming every orbit is circular is wrong because many useful spacecraft paths are elliptical and have changing altitude and speed.
Practice Questions
- 1 A satellite has a perigee altitude of 400 km and an apogee altitude of 2000 km. Using Earth’s radius as 6371 km, find the perigee radius and apogee radius measured from Earth’s center.
- 2 An elliptical orbit has semi-major axis a = 10000 km and eccentricity e = 0.20. Calculate r_p = a(1 - e) and r_a = a(1 + e).
- 3 A spacecraft in an elliptical orbit fires its engine at perigee to increase its speed. Explain what happens to the opposite side of the orbit and why this maneuver is useful.