Astrophysics (Index)About

semi-major axis

(a)
(maximum radius of an ellipse)

An ellipse's semi-major axis (a) is half the distance between the ellipse's furthest two points, or equivalently, the distance from the ellipse's center to one of its points furthest from the center. The semi-minor axis (b) is an analogous distance from the ellipse's center to one of the ellipse's points nearest the center. They are mathematically related with e, the ellipse's eccentricity:

b = a (1 - e2)0.5

The semi-major axis can be used in various orbital calculations. For example, for an orbit:

T = 2π(a3/μ)0.5

Where:

(All these equations apply to a circle as well, taking its radius as both its semi-major axis and its semi-minor axis.) The semi-major axis is useful for characterizing the size of an orbit; the term orbital radius is clearly useful for circular orbits and useful to indicate an approximation of an orbit that is not far from circular, but its meaning is vague regarding decidedly eccentric orbits.

When an orbit is viewed in the sky, only a projection of it is observed, based upon the orbital inclination, typically unknown, and often what is evident is a lower bound on the semi-major axis. Sometimes, a likely semi-major axis is cited based upon the average of possible semi-major axes, assuming a randomly positioned orbital plane positioning and some knowledge of the observational error distribution. The actual orbit can be worked out with sufficient data on the position of the host in relation to the projection, and/or on the projected orbital speed throughout the orbit.


(orbits,celestial mechanics,measure)
Further reading:
https://en.wikipedia.org/wiki/Semi-major_axis
https://astronomy.swin.edu.au/cosmos/s/Semi-major+Axis
http://hyperphysics.phy-astr.gsu.edu/hbase/Math/ellipse.html
https://dictionary.obspm.fr/index.php/index.php?showAll=1&formSearchTextfield=semi-major+axis

Referenced by pages:
51 Eridani b
51 Pegasi b (51 Peg b)
55 Cancri e (55 Cnc e)
barycenter
Beta Pictoris b (β Pic b)
Ceres
circumbinary planet
Earth
GJ 1132 b
GJ 1214 b
Gliese 436 b (GJ 436 b)
HAT-P-7b
HD 189733 b
HD 209458 b
HD 80606 b
Hill radius
Holmberg radius (RH)
hyperfine structure
Jupiter
K2-18b
Kepler's laws
Kepler-1625b
Kepler-16b
Kepler-186f
Kepler-452b
Kepler-79
Laplace radius (rL)
LHS 3844 b
Mars
mean anomaly
Mercury
moon
near-Earth object (NEO)
Neptune
OGLE-2005-BLG-390Lb
Planet Nine
Pluto
projected semi-major axis
Proxima b
Psyche
radial velocity method
Saturn
synchronous orbit
Titius-Bode law
TOI 700 d
trans-Neptune object (TNO)
TRAPPIST-1
Uranus
Venus
WASP-12b
WASP-33b
WASP-43b
WASP-67b
XO-3b

Index