The Ultimate Elliptic orbit Dog Breeds Information Guide and Reference

(Redirected from Elliptical orbit)

In astrodynamics or celestial mechanics a elliptic orbit is an orbit with the eccentricity greater than 0 and less than 1.

Specific energy of an elliptical orbit is negative.

Contents

1 Velocity

Velocity

Under standard assumptions the orbital velocity ( $v\,$ ) of a body traveling along elliptic orbit can be computed as:

$v=\sqrt{2\mu\left({1\over{r}}-{1\over{2a}}\right)}$

where:

Conclusion:

Velocity does not depend on eccentricity but is determined by length of semi-major axis ( $a\,\!$ ),
Velocity equation is similar to that for hyperbolic trajectory with the difference that for the latter one ${1\over{2a}}$ is positive.

Under standard assumptions the orbital period ( $T\,\!$ ) of a body traveling along elliptic orbit can be computed as:

$T={2\pi\over{\sqrt{\mu}}}a^{3\over{2}}$

where:

Conclusions:

The orbital period is equal to that for a circular orbit with the orbit radius equal to the semi-major axis ( $a\,\!$ ),
The orbital period does not depend on the eccentricity (See also: Kepler's third law).

Under standard assumptions, specific orbital energy ( $\epsilon\,$ ) of elliptic orbit is negative and the orbital energy conservation equation for this orbit takes form:

${v^2\over{2}}-{\mu\over{r}}=-{\mu\over{2a}}=\epsilon<0$

where:

Conclusions:

Specific energy for elliptic orbits is independent of eccentricity and is determined only by semi-major axis of the ellipse.

Using the virial theorem we find:

the time-average of the specific potential energy is equal to 2ε
- the time-average of r^-1 is a^-1
the time-average of the specific kinetic energy is equal to -ε

This section is a stub. You can help Wikipedia by expanding it.

In the solar system planets, asteroids, comets and space debris have elliptical orbits around the Sun.

Moons have an elliptic orbit around their planet.

Many artificial satellites have various elliptic orbits around the Earth.