Editing Orbital speed (section)

==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 {{math|''μ''}} is the [[standard gravitational parameter]] of the orbited body, {{math|''r''}} is the distance at which the speed is to be calculated, and {{math|''a''}} is the length of the semi-major axis of the elliptical orbit. This expression is called the [[vis-viva equation]].<ref name="lissauer2019" />

For the Earth at [[perihelion]], the value is:

:<math> \sqrt {1.327 \times 10^{20} ~\text{m}^3 \text{s}^{-2} \cdot \left({2 \over 1.471 \times 10^{11} ~\text{m}} - {1 \over 1.496 \times 10^{11} ~\text{m}}\right)} \approx 30,300 ~\text{m}/\text{s}</math>

which is slightly faster than Earth's average orbital speed of {{convert|29,800|m/s|mph|abbr=on}}, as expected from [[Kepler's laws of planetary motion#Second law|Kepler's 2nd Law]].

{{earth orbits}}