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 2 Orbital period 3 Energy 4 Flight path angle 5 Equation of motion 6 Orbital parameters

Velocity

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

where:

• is standard gravitational parameter,
• is radial distance of orbiting body from central body,
• is length of semi-major axis.

Conclusion:

• Velocity does not depend on eccentricity but is determined by length of semi-major axis (),
• Velocity equation is similar to that for hyperbolic trajectory with the difference that for the latter one is positive.

Orbital period

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

where:

• is standard gravitational parameter,
• is length of semi-major axis.

Conclusions:

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

Energy

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

where:

• is orbital velocity of orbiting body,
• is radial distance of orbiting body from central body,
• is length of semi-major axis,
• is standard gravitational parameter.

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

Flight path angle

Equation of motion

See orbit equation.

Orbital parameters

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