Perigee and
Apogee

Perigee is the point where an orbiting object is closest to the center of Earth. Apogee is the point where it is farthest from Earth's center. Together they are the orbit's apsides, the two turning points of radial distance in a bound elliptical orbit.

The names depend on the central body. Periapsis and apoapsis are the general terms. Around Earth, they become perigee and apogee. Around the Sun, they are perihelion and aphelion. The underlying geometry is the same: one point minimizes orbital radius and the opposite point maximizes it.

A perfectly circular orbit is a limiting case. Its eccentricity is zero, its radius is constant, and every point is equally near to Earth. Perigee and apogee then have the same radius and altitude, so the labels no longer identify visibly different parts of the path. Real operational orbits are rarely perfect circles, although many are close enough that the difference is small.

Kepler's first law states that a bound two-body orbit is an ellipse with the attracting body at one focus. For an Earth satellite, Earth's center occupies one focus of the ellipse. The geometric center of the ellipse lies somewhere else, and the second focus is empty. This offset is the reason the satellite-to-Earth distance changes around the orbit.

The ellipse is described by its semi-major axis a and eccentricity e. The semi-major axis sets the orbit's overall size. Eccentricity describes how far the shape departs from a circle: zero is circular, while values closer to one produce a more elongated bound ellipse.

The geocentric radii at the apsides are r_p = a(1 - e) and r_a = a(1 + e). These are measured from Earth's center, not from the surface. The diagram enlarges Earth and the satellite so the structure remains readable; it does not claim a scale model.

Orbital equations usually use radius r, measured from Earth's center of mass. Websites and mission descriptions often report altitude h, measured above a reference Earth surface. They are connected by h = r - R_E, where R_E is the chosen Earth radius.

This distinction matters whenever values enter an equation. A “400 km orbit” does not have a geocentric radius of 400 km. Using an equatorial Earth radius of 6,378.137 km, its radius is about 6,778.137 km. Substituting altitude where radius is required produces a physically meaningless speed or period.

Earth is not a perfect sphere, so precise operations may use an ellipsoid, geodetic altitude, or a mission-specific reference. Introductory two-body calculations commonly use a representative spherical radius. The convention must be stated because a tracker, an orbital element set, and a map can use related but not identical altitude definitions.

A satellite in an unpowered elliptical orbit continuously exchanges gravitational potential energy and kinetic energy. As it falls inward toward perigee, gravitational potential energy decreases while kinetic energy increases. The satellite accelerates and reaches its maximum orbital speed at perigee. As it climbs outward toward apogee, kinetic energy is converted back into potential energy, so the satellite slows down.

The total specific mechanical energy remains constant in the ideal two-body model. The vis-viva equation, v = sqrt[mu(2/r - 1/a)], makes the relationship explicit. The gravitational parameter mu and semi-major axis a are fixed for one ideal orbit. When radius r is smaller, the speed v is larger; when r is larger, v is smaller.

This does not mean gravity is absent at apogee or overwhelming only at perigee. Gravity acts everywhere. What changes is the satellite's position and velocity within one conserved-energy trajectory. Perigee and apogee are also the places where radial velocity is momentarily zero: the satellite stops moving inward or outward and reverses that radial trend, while continuing tangentially along the orbit.

Kepler's second law says that a line joining the satellite and Earth sweeps out equal areas in equal time intervals. Near perigee, the radius is short. To sweep the same area during a fixed time, the satellite must cover a longer arc and therefore move faster. Near apogee, the radius is long, so the same area can be swept while the satellite covers a shorter arc and moves more slowly.

The equal-area statement is stronger than a decorative diagram. It expresses conservation of specific angular momentum in the ideal two-body problem. At perigee and apogee the velocity is perpendicular to the radius vector, giving the useful relationship r_pv_p = r_av_a. Therefore v_p/v_a = r_a/r_p.

That inverse ratio applies directly at the two apsides because radius and velocity are perpendicular there. It should not be generalized carelessly to every point in the orbit, where the velocity can also have a radial component. The verified sectors below are calculated from equal time intervals rather than drawn by eye.

Consider an ideal Earth orbit with a perigee altitude of 400 km and an apogee altitude of 2,000 km. Using an Earth radius of 6,378.137 km gives r_p = 6,778.137 km and r_a = 8,378.137 km. The semi-major axis is their average, 7,578.137 km, and the eccentricity is approximately 0.1056.

With Earth's standard gravitational parameter of 398,600.4418 km³/s², vis-viva gives a perigee speed of about 8.06 km/s and an apogee speed of about 6.52 km/s. The orbital period is approximately 109.4 minutes. The speed ratio, 8.06/6.52, matches the radius ratio, 8,378.137/6,778.137, to rounding precision.

The plotted curves cover the half-orbit from perigee to apogee. Altitude rises continuously while speed falls continuously. During the return half, the process reverses: altitude falls and speed rises until the satellite reaches perigee again. Real trajectories include oblateness, drag, third-body gravity, radiation pressure, and maneuvers, but the two-body pattern remains the essential foundation.

A short tangential burn at an apsis changes orbital energy while the spacecraft is already at an extreme radius. A prograde burn at perigee raises the opposite side of the orbit, increasing apogee. A retrograde burn at perigee lowers apogee. Likewise, a prograde burn at apogee raises perigee, while a retrograde burn lowers it.

This is the logic behind a Hohmann transfer. The first burn changes one apsis to enter a transfer ellipse; the spacecraft coasts to the opposite apsis; the second burn changes the other side and circularizes the orbit. The burns are not “pushing the satellite upward” in a straight line. They change velocity and therefore reshape the entire future trajectory.

Real mission design also considers inclination, argument of perigee, atmospheric clearance, eclipses, communication geometry, propulsion limits, and collision risk. A burn away from an apsis can change both apsidal radii and rotate the line of apsides. The simple rule is valuable, but it is the beginning of maneuver design rather than a complete flight plan.

In a pure two-body model, the ellipse remains fixed. Around the real Earth, perturbations change its size, shape, and orientation. Earth's equatorial bulge produces secular rotation of the orbital plane and line of apsides. Atmospheric drag removes energy, especially when perigee enters denser upper atmosphere. The Moon, Sun, solar radiation pressure, attitude changes, and propulsion also contribute.

Drag does not simply lower every point by the same amount. Energy loss near perigee can reduce the opposite side strongly, gradually circularizing some decaying orbits before final reentry. For highly eccentric missions, operators monitor perigee altitude carefully because a relatively small reduction can move the spacecraft into much denser atmosphere.

Orbital element products may report values associated with a model, an epoch, or a mean orbit. A continuously propagated instantaneous trajectory can have slightly different extrema. When comparing two sources, check their epoch, reference frame, gravity model, Earth radius convention, and whether the elements are mean or osculating.

Jewawud Orbital Tracker (JOT) displays public satellite positions and helps visitors inspect changing altitude, speed, and three-dimensional orbital geometry. For an eccentric orbit, repeated observation can reveal the same qualitative pattern shown here: faster motion at lower radius and slower motion at higher radius.

JOT uses public orbital data for education and visualization. It is not precision flight dynamics, and a displayed value should not be treated as an operator-grade maneuver input. Public TLE data represent a mean model designed for SGP4 propagation; derived extrema can change with the data epoch and propagation method.

The Orbital Planner is useful for controlled comparison. Set different perigee and apogee altitudes, then compare eccentricity, period, and speed. Keep radius and altitude distinct, and remember that diagrams commonly enlarge Earth and spacecraft while compressing orbital distances to remain legible.

“Earth sits at the center of every orbit.” Only a circular orbit places the central body at the geometric center. In an ellipse, Earth occupies one focus.

“The satellite nearly stops at apogee.” No. It reaches its minimum speed for that orbit but continues moving tangentially.

“Perigee altitude can be inserted directly into vis-viva as r.” No. Vis-viva uses geocentric radius, so the chosen Earth radius must be added first.

“A higher satellite is always in a different orbit.” One eccentric orbit includes a continuous range of altitudes from perigee to apogee.

“Equal areas mean equal arc lengths.” The opposite is generally true in an ellipse: equal times produce a longer arc near perigee and a shorter arc near apogee.

What is the generic name for perigee? Periapsis. Apogee's generic counterpart is apoapsis.

Where is a satellite fastest? At perigee in an elliptical Earth orbit.

Where is it slowest? At apogee.

Can perigee and apogee be equal? Yes. They are equal for a circular orbit.

Does a burn at perigee raise perigee? An instantaneous tangential burn at perigee primarily changes the opposite apsis, apogee. A later burn at apogee can then raise perigee.

NASA Science: Orbits and Kepler's Laws - ellipse geometry and the three laws of orbital motion.

NASA Basics of Space Flight: Gravity and Mechanics - acceleration, orbital velocity, and Kepler's laws.

NASA GSFC: More on Kepler's Second Law - velocity and radius relationships at perigee and apogee.

NASA/JPL Fundamentals of Orbital Mechanics - vis-viva and two-body trajectory relationships.

ESA Launchers FAQ - Earth-orbit definitions of perigee and apogee.