Orbital speed

Orbital speed

The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body. It can be used to refer to either the mean orbital speed, the average speed as it completes an orbit, or instantaneous orbital speed, the speed at a particular point in its orbit.

The orbital speed at any position in the orbit can be computed from the distance to the central body at that position, and the specific orbital energy, which is independent of position: the kinetic energy is the total energy minus the potential energy.

Contents

Radial trajectories

In the case of radial motion:

  • If the energy is non-negative: The orbit is open. The motion is either directly towards or away from the other body, the motion never stops or reverses direction. See radial hyperbolic trajectory
  • For the zero-energy case, see radial parabolic trajectory.
  • If the energy is negative: The orbit is closed. The motion can be first away from the central body, up to r=μ/|ε| (apoapsis), then falling back. This is the limit case of an orbit which is part of an ellipse with eccentricity tending to 1, and the other end of the ellipse tending to the center of the central body. See radial elliptic trajectory, radial trajectories, free-fall time.

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 means that the body moves faster near its periapsis than near its apoapsis, because at the smaller distance it needs to trace a greater arc to cover the same area. This law is usually stated as "equal areas in equal time."

Mean orbital speed

For orbits with small eccentricity, the length of the orbit is close to that of a circular one, and the mean orbital speed can be approximated either from observations of the orbital period and the semimajor axis of its orbit, or from knowledge of the masses of the two bodies and the semimajor axis.

v_o \approx {2 \pi a \over T}
v_o \approx \sqrt{\mu \over a}

where v_o\,\! is the orbital velocity, a\,\! is the length of the semimajor axis, T\,\! is the orbital period, and \mu\,\! is the standard gravitational parameter. Note that this is only an approximation that holds true when the orbiting body is of considerably lesser mass than the central one, and eccentricity is close to zero.

Taking into account the mass of the orbiting body,

v_o \approx \sqrt{m_2^2 G \over (m_1 + m_2) r}

where m_1\,\! is now the mass of the body under consideration, m_2\,\! is the mass of the body being orbited, r\,\! is specifically the distance between the two bodies (which is the sum of the distances from each to the center of mass), and G\,\! is the gravitational constant. This is still a simplified version; it doesn't allow for elliptical orbits, but it does at least allow for bodies of similar masses.

When one of the masses is almost negligible compared to the other mass as the case for Earth and Sun, one can approximate the previous formula to get:

v_o \approx \sqrt{\frac{GM}{r}}

or

v_o \approx \frac{v_e}{\sqrt{2}}

Where M is the (greater) mass around which this negligible mass or body is orbiting, and ve is the escape velocity.

For an object in an eccentric orbit orbiting a much larger body, the length of the orbit decreases with eccentricity e\,\!, and is given at ellipse. This can be used to obtain a more accurate estimate of the average orbital speed:

 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 - \dots \right] [1]

The mean orbital speed decreases with eccentricity.

Earth orbits

orbit center-to-center
distance
altitude above
the Earth's surface
speed period/time in space specific orbital energy
minimum sub-orbital spaceflight (vertical) 6,500 km 100 km 0.0 km/s just reaching space -61.3 MJ/kg
ICBM up to 7,600 km up to 1,200 km 6 to 7 km/s time in space: 25 min -27.9 MJ/kg
Low Earth orbit 6,600 to 8,400 km 200 to 2,000 km circular orbit: 6.9 to 7.8 km/s
elliptic orbit: 6.5 to 8.2 km/s
89 to 128 min -17.0 MJ/kg
Molniya orbit 6,900 to 46,300 km 500 to 39,900 km 1.5 to 10.0 km/s 11 h 58 min -4.7 MJ/kg
GEO 42,000 km 35,786 km 3.1 km/s 23 h 56 min -4.6 MJ/kg
Orbit of the Moon 363,000 to 406,000 km 357,000 to 399,000 km 0.97 to 1.08 km/s 27.3 days -0.5 MJ/kg

See also

References

  1. ^ Horst Stöcker, John W. Harris (1998). Handbook of Mathematics and Computational Science. Springer. pp. 386. ISBN 0387947469. 

Wikimedia Foundation. 2010.

Игры ⚽ Нужна курсовая?

Look at other dictionaries:

  • Orbital — may refer to: In chemistry and physics: Atomic orbital Molecular orbital In astronomy and space flight: Orbit Orbital resonance Orbital period Orbital plane (astronomy) Orbital elements Orbital speed Orbital maneuver Orbital spaceflight In… …   Wikipedia

  • Orbital elements — are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are generally considered in classical two body systems, where a Kepler orbit is used (derived from Newton s laws of motion and Newton s law… …   Wikipedia

  • Orbital inclination change — is an orbital maneuver aimed at changing the inclination of an orbiting body s orbit. This maneuver is also known as an orbital plane change as the plane of the orbit is tipped. This maneuver requires a change in the orbital velocity vector… …   Wikipedia

  • Orbital decay — is the process of prolonged reduction in the altitude of a satellite s orbit. This can be due to drag produced by an atmosphere due to frequent collisions between the satellite and surrounding air molecules. The drag experienced by the object is… …   Wikipedia

  • Orbital velocity — can refer to the following: The orbital speed of a body in a gravitational field. The velocity of particles due to wave motion, in particular in wind waves. The equivalent velocity of a bound electron needed to produce its orbital kinetic energy …   Wikipedia

  • Orbital mechanics — A satellite orbiting the earth has a tangential velocity and an inward acceleration. Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other… …   Wikipedia

  • Orbital spaceflight — Discovery rockets to orbital velocity, seen here just after booster separation An orbital spaceflight (or orbital flight) is a spaceflight in which a spacecraft is placed on a trajectory where it could remain in space for at least one orbit. To… …   Wikipedia

  • Orbital ring — An Orbital Ring is a concept for a space elevator that consists of a ring in low earth orbit that rotates at above orbital speed, that has fixed tethers hanging down to the ground. The structure is intended to be used for space launch. The… …   Wikipedia

  • Orbital period — For the music album, see Orbital Period (album). The orbital period is the time taken for a given object to make one complete orbit about another object. When mentioned without further qualification in astronomy this refers to the sidereal period …   Wikipedia

  • Orbital maneuver — In spaceflight, an orbital maneuver is the use of propulsion systems to change the orbit of a spacecraft. For spacecraft far from Earth for example those in orbits around the Sun an orbital maneuver is called a deep space maneuver (DSM).[not… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”