How Is the Period of a Hohmann Transfer Orbit Calculated?

[tandoorichicken]

How do you calculate the period of orbit for an elliptical orbit, ie, a Hohmann transfer?

 

[enigma]

Period is only dependant on the semimajor axis. Eccentricity doesn't matter.

P = 2 * \pi * \sqrt{\frac{a^3}{\mu}}

 

[M98Ranger]

A Hohmann transfer orbit is a type of orbital maneuver used to transfer a spacecraft from one circular orbit to another. It involves using the gravitational pull of a planet to change the spacecraft's trajectory and reach its desired destination.

To calculate the period of an elliptical orbit, including a Hohmann transfer, we can use the following formula:

T = 2π √(a^3/μ)

Where T is the period of the orbit in seconds, a is the semi-major axis of the ellipse, and μ is the standard gravitational parameter of the central body (planet).

In a Hohmann transfer, the spacecraft's orbit will change from a circular orbit with a radius of r1 to an elliptical orbit with a semi-major axis of a2. The semi-major axis can be calculated using the following formula:

a2 = (r1 + r2)/2

Where r2 is the radius of the destination circular orbit.

Plugging this value into the first formula, we can calculate the period of the elliptical orbit, which will also be the duration of the Hohmann transfer.

It is important to note that this calculation assumes a perfectly circular and unperturbed orbit. In reality, factors such as atmospheric drag, solar radiation pressure, and gravitational influences from other bodies may affect the spacecraft's orbit and its period. Therefore, this calculation is an approximation and may need to be adjusted for more accurate results.