Site Map
  Orbital Speed Index for
Orbital 		Website Links For
Orbital 		 

Information About

Orbital Speed
APPAREL
BABY
BEAUTY
BOOKS
CAR TOYS
CELL PHONES
DVD'S
ELECTRONICS
GOURMET FOOD
GROCERIES
HEALTH & PERSONAL
HOME & GARDEN
JEWELRY
MUSIC
MUSIC INSTRUMENTS
OFFICE PRODUCTS
SOFTWARE
SPORTING GOODS
TOOLS & HARDWARE
TOYS
VIDEO GAMES
SHOPPING HOME
MORE SHOPPING...



The orbital speed at any position in the orbit can be computed from the distance to the central body at that position, and the is the total energy minus the Potential Energy .

Thus, under Standard Assumptions the orbital speed (v\,) is:

  • in general: v=

    • \sqrt{2\left({\mu\over{r}}+{\epsilon} ight)}


  • --- Elliptic Orbit : v=

    • \sqrt{\mu\left({2\over{r}}-{1\over{a}} ight)}






Radial trajectories


In the case of radial motion:
  • if the energy is non-negative: the motion is either for the whole trajectory away from the central body, or for the whole trajectory towards it. For the zero-energy case, see Escape Orbit and Capture Orbit .

  • if the energy is negative: the motion can be first away from the central body, up to r=μ/|ε|, 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.



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 Mass es 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, and r\,\! is specifically the distance between the two bodies (which is the sum of the distances from each to the center of mass). This is still a simplified version; it doesn't allow for Elliptical orbits, but it does at least allow for bodies of similar masses.

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 - \dots ight

The mean orbital speed decreases with eccentricity.

See also Examples .