In gravitationally bound systems, the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter (the combined center of mass) or, if one body is much more massive than the other bodies of the system combined, its speed relative to the center of mass of the most massive body.
The term can be used to refer to either the mean orbital speed (i.e. the average speed over an entire orbit) or its instantaneous speed at a particular point in its orbit. The maximum (instantaneous) orbital speed occurs at periapsis (perigee, perihelion, etc.), while the minimum speed for objects in closed orbits occurs at apoapsis (apogee, aphelion, etc.). In ideal two-body systems, objects in open orbits continue to slow down forever as their distance to the barycenter increases.
When a system approximates a two-body system, instantaneous orbital speed at a given point of the orbit can be computed from its distance to the central body and the object's specific orbital energy, sometimes called "total energy". Specific orbital energy is constant and independent of position.
- If the specific orbital energy is positive the orbit is unbound, or open, and will follow a hyperbola with the larger body the focus of the hyperbola. Objects in open orbits do not return; once past periapsis their distance from the focus increases without bound. See radial hyperbolic trajectory
- If the total energy is zero, (E<sub>k</sub> = E<sub>p</sub>): the orbit is a parabola with focus at the other body. See radial parabolic trajectory. Parabolic orbits are also open.
- If the total energy is negative, : The orbit is bound, or closed. The motion will be on an ellipse with one focus at the other body. See radial elliptic trajectory, free-fall time. Planets have bound orbits around the Sun.
Transverse orbital speed
The transverse orbital speed is inversely proportional to the distance to the central body because of the law of conservation of angular momentum, or equivalently, Kepler's second law. This states that as a body moves around its orbit during a fixed amount of time, the line from the barycenter to the body sweeps a constant area of the orbital plane, regardless of which part of its orbit the body traces during that period of time.
This law implies that the body moves slower near its apoapsis than near its periapsis, because at the smaller distance along the arc it needs to move faster to cover the same area.
:<math>v \approx {2 \pi a \over T} \approx \sqrt{\mu \over a}</math>
where is the orbital velocity, is the length of the semimajor axis, is the orbital period, and is the standard gravitational parameter. This is an approximation that only holds true when the orbiting body is of considerably lesser mass than the central one, and eccentricity is close to zero.
When one of the bodies is not of considerably lesser mass see: Gravitational two-body problem
So, when one of the masses is almost negligible compared to the other mass, as the case for Earth and Sun, one can approximate the orbit velocity <math>v_o</math> as:
:<math> v_o = \frac{2\pi a}{T}\left[1-\frac{1}{4}e^2-\frac{3}{64}e^4 -\frac{5}{256}e^6 -\frac{175}{16384}e^8 - \cdots \right] </math>
The mean orbital speed decreases with eccentricity.
Instantaneous orbital speed
For the instantaneous orbital speed of a body at any given point in its trajectory, both the mean distance and the instantaneous distance are taken into account:
:<math> v = \sqrt {\mu \left({2 \over r} - {1 \over a}\right)}</math>
where is the standard gravitational parameter of the orbited body, is the distance at which the speed is to be calculated, and is the length of the semi-major axis of the elliptical orbit. This expression is called the vis-viva equation.
{| class="wikitable sortable"
|+ Orbital periods and velocities of the planets
! Planet
! Orbital period (days)
! Orbital period (Earth years)
! Orbital velocity
|-
| Mercury
| 87.969
| 0.241
| 47.9 km/s (29.8 mi/s)
|-
| Venus
| 224.701
| 0.615
| 35.0 km/s (21.7 mi/s)
|-
| Earth
| 365.256
| 1.000
| 29.8 km/s (18.5 mi/s)
|-
| Mars
| 686.980
| 1.881
| 24.1 km/s (15.0 mi/s)
|-
| Jupiter
| 4,332.589
| 11.862
| 13.1 km/s (8.1 mi/s)
|-
| Saturn
| 10,759.22
| 29.457
| 9.7 km/s (6.0 mi/s)
|-
| Uranus
| 30,688.5
| 84.020
| 6.8 km/s (4.2 mi/s)
|-
| Neptune
| 60,182
| 164.8
| 5.4 km/s (3.4 mi/s)
|}
Halley's Comet on an eccentric orbit that reaches beyond Neptune will be moving 54.6 km/s when from the Sun, 41.5 km/s when 1 AU from the Sun (passing Earth's orbit), and roughly 1 km/s at aphelion from the Sun. Objects passing Earth's orbit going faster than 42.1 km/s have achieved escape velocity and will be ejected from the Solar System if not slowed down by a gravitational interaction with a planet.
{|class="wikitable sortable" style="text-align:center; font-size:0.9em;"
|+Velocities of better-known numbered objects that have perihelion close to the Sun
! Object
! Velocity at perihelion
! Velocity at 1 AU<br/>(passing Earth's orbit)
|-
| 322P/SOHO || 181 km/s @ 0.0537 AU || 37.7 km/s
|-
| 96P/Machholz || 118 km/s @ 0.124 AU || 38.5 km/s
|-
| 3200 Phaethon || 109 km/s @ 0.140 AU || 32.7 km/s
|-
| 1566 Icarus || 93.1 km/s @ 0.187 AU || 30.9 km/s
|-
| 66391 Moshup || 86.5 km/s @ 0.200 AU || 19.8 km/s
|-
| 1P/Halley || 54.6 km/s @ 0.586 AU || 41.5 km/s
|}
See also
- Escape velocity
- Delta-v budget
- Hohmann transfer orbit
- Bi-elliptic transfer
References
hu:Kozmikus sebességek#Szökési sebességek