Enter the gravitational parameter of the central body, the initial radius of the transfer orbit, and the semi-major axis of the transfer orbit into the calculator to determine the delta-v required for a Hohmann Transfer; this calculator can also evaluate any of the variables given the others are known.
Hohmann Transfer Formula
The following formula is used to calculate the delta-v required for a Hohmann Transfer:
Δv = sqrt(mu * ((2 / r1) - (1 / a)))
Variables:
- Δv is the delta-v required for the Hohmann Transfer
- mu is the gravitational parameter of the central body
- r1 is the initial radius of the transfer orbit
- a is the semi-major axis of the transfer orbit
To calculate the delta-v required for a Hohmann Transfer, multiply the gravitational parameter of the central body by the difference between 2 divided by the initial radius of the transfer orbit and 1 divided by the semi-major axis of the transfer orbit. Take the square root of the result.
What is a Hohmann Transfer?
A Hohmann Transfer is a method of moving a spacecraft from one orbit to another, typically used for transferring between different planetary orbits. Named after Walter Hohmann, the German scientist who first described it in 1925, the Hohmann Transfer involves two stages of propulsion. The first stage propels the spacecraft from its initial orbit into a transfer orbit, which is an elliptical path that intersects both the initial and final orbits. At the point where the transfer orbit intersects the final orbit, the spacecraft is propelled again to match the speed and direction of the final orbit. This method is energy-efficient, requiring the least amount of propellant compared to other transfer methods, but it also takes the longest time.
How to Calculate Hohmann Transfer?
The following steps outline how to calculate the Hohmann Transfer:
- First, determine the initial orbit radius (R1) and the final orbit radius (R2).
- Next, calculate the semi-major axis of the transfer ellipse using the formula: a = (R1 + R2) / 2.
- Then, calculate the velocity of the transfer ellipse at the initial orbit using the formula: V1 = sqrt(mu / R1), where mu is the gravitational parameter of the central body.
- Next, calculate the velocity of the transfer ellipse at the final orbit using the formula: V2 = sqrt(mu / R2).
- Then, calculate the delta-v required for the transfer using the formula: delta-v = V2 – V1.
- Finally, calculate the time of flight for the transfer using the formula: T = pi * sqrt(a^3 / mu).
Example Problem:
Use the following variables as an example problem to test your knowledge:
Initial orbit radius (R1) = 8000 km
Final orbit radius (R2) = 12000 km
Gravitational parameter (mu) = 3.986 x 10^5 km^3/s^2
