A semimajor axis is half the longest diameter of an ellipse, measured from the center to the farthest edge. In astronomy, it’s one of the most important numbers describing any orbit, because it tells you the average distance between an orbiting body and the thing it orbits. Earth’s semimajor axis, for example, is about 149.6 million kilometers, which defines the astronomical unit (AU) used to measure distances across the solar system.
The Geometry Behind It
An ellipse looks like a stretched circle. It has two axes: a long one and a short one. The full long axis runs from one end of the ellipse to the other through the center, and the semimajor axis is exactly half of that. The shorter half-width is called the semiminor axis. Together with two special interior points called foci, the semimajor axis completely defines the shape and size of any ellipse.
If the semimajor axis and semiminor axis are equal, the ellipse becomes a perfect circle, and the semimajor axis is simply the radius. The more the two axes differ, the more elongated (or “eccentric”) the ellipse becomes.
Why It Matters in Orbits
Planets, moons, asteroids, and satellites all travel in elliptical paths. The body they orbit sits at one of the ellipse’s two foci, not at the center. This means the orbiting object is sometimes closer and sometimes farther away. The semimajor axis represents the average of those distances, which is why NASA defines it as “the mean distance from the Sun” for objects orbiting our star.
Because orbits aren’t perfect circles, simply saying “distance from the Sun” can be misleading. Mars, for instance, swings between about 207 million km at its closest approach and 249 million km at its farthest. The semimajor axis captures the characteristic size of that orbit in a single number: 1.524 AU.
The Link to Orbital Period
The semimajor axis doesn’t just describe an orbit’s size. It also determines how long one trip around that orbit takes. Kepler’s Third Law states that the square of an object’s orbital period is directly proportional to the cube of its semimajor axis. In plain terms: a larger orbit means a dramatically longer year. Double the semimajor axis and the orbital period increases by a factor of about 2.8.
This relationship is why Neptune, with a semimajor axis of roughly 30 AU, takes about 165 Earth years to complete one orbit, while Mercury at 0.387 AU zips around in just 88 days. The semimajor axis is the single variable that controls this timing.
Energy and the Semimajor Axis
There’s a deeper physical reason the semimajor axis is so central to orbital mechanics: it’s directly tied to the total energy of the orbit. The total mechanical energy of an orbiting body (its combined kinetic and gravitational potential energy) depends only on the semimajor axis, not on how elongated the orbit is. Two orbits with identical semimajor axes but very different shapes have the same total energy.
This is why changing a spacecraft’s orbit always comes down to changing its semimajor axis. Firing engines to speed up increases the total energy, which expands the semimajor axis and raises the orbit. Slowing down shrinks it.
How to Calculate It
The simplest way to find the semimajor axis is from the closest and farthest points of an orbit. Add the nearest distance (periapsis) to the farthest distance (apoapsis), then divide by two. For Earth orbiting the Sun, that’s roughly (147.1 million km + 152.1 million km) / 2 = 149.6 million km.
If you know the eccentricity (a number between 0 and 1 that describes how stretched the ellipse is) and the closest approach distance, you can also work backward. The periapsis equals the semimajor axis multiplied by (1 minus the eccentricity), so dividing the periapsis by that factor gives you the semimajor axis.
Semimajor Axes of the Planets
Here are the semimajor axes of all eight planets, based on data from NASA’s Jet Propulsion Laboratory:
- Mercury: 0.387 AU (57.9 million km)
- Venus: 0.723 AU (108.2 million km)
- Earth: 1.000 AU (149.6 million km)
- Mars: 1.524 AU (227.9 million km)
- Jupiter: 5.203 AU (778.5 million km)
- Saturn: 9.537 AU (1,426.7 million km)
- Uranus: 19.189 AU (2,870.7 million km)
- Neptune: 30.070 AU (4,498.4 million km)
Notice how the gaps between planets grow enormously as you move outward. Neptune’s semimajor axis is nearly 78 times larger than Mercury’s.
Satellite Orbits Around Earth
The semimajor axis is equally important for artificial satellites. A geostationary satellite, the kind that provides weather imagery and TV signals from a fixed point in the sky, requires a very specific semimajor axis of about 42,164 km from Earth’s center (roughly 35,786 km above the surface). At that exact distance, the orbital period matches Earth’s 24-hour rotation, keeping the satellite stationary relative to the ground.
Low-Earth orbit satellites like the International Space Station have a much smaller semimajor axis of around 6,780 km from Earth’s center, giving them an orbital period of roughly 90 minutes. GPS satellites sit in between at about 26,560 km, orbiting twice per day. In every case, the semimajor axis is what sets the orbital period and determines the satellite’s function.