Hohmann Transfer Calculator
The Hohmann Transfer orbit is a cost-effective technique for transferring a spacecraft between two circular orbits. The Hohmann transfer orbit involves two propulsion maneuvers: the first propels the spacecraft into an elliptical transfer orbit, and the second adjust it to achieve a circular orbit at the desired altitude.
The Hohmann transfer is commonly used for orbital maneuvers, especially when transferring between low Earth orbit (LEO) and geostationary orbit (GEO) or other orbits at varying altitudes.
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ΔV1 = √ (μ / r1) * (√ ((2 * r2) / (r1 + r2)) - 1))
ΔV2 = √ (μ / r2) * (1-√ ((2 * r1) / (r1 + r2)))
r1: Initial Orbit Radius
r2: Final Orbit Radius
μ: The standard gravitational parameter of Earth and value of μ is 3.986004418*105 Km3/s2
A Hohmann transfer involves two key velocity changes (impulses) that places the spacecraft on an elliptical orbit and touches both the starting and target circular orbits. The primary steps include:
First Impulse:
The spacecraft is initially in the lower orbit (usually circular). The first burn accelerates the spacecraft, putting it into an elliptical orbit, with the apogee (farthest point) reaching the target orbit.
Second Impulse:
At the apogee of the elliptical orbit, a second burn is performed to circularize the orbit, transitioning the spacecraft into the target orbit.
For Example: If r1 be 1000 Km, r2 be 2000 Km, and μ is 3.986004418*105 Km3/s2 then Hohmann Transfer, Delta V is
ΔV1 = √ (μ / r1) * (√ ((2 * r2) / (r1 + r2)) - 1))
ΔV1 = √ (3.986004418*105 /1000 ) * (√ ((2 * 2000 ) / (1000 +2000 )) - 1))
ΔV1 = 3.08859321 Km/s
ΔV2 = √ (μ / r2) * (1-√ ((2 * r1) / (r1 + r2)))
ΔV2 = √ (3.986004418*105 /2000 ) * (1-√ ((2 *1000 ) / (1000 + 2000)))
ΔV2 = 2.59058622 Km/s
ΔVTotal = ΔV1 + ΔV2
ΔVTotal = 3.08859321 + 2.59058622
ΔVTotal = 5.67917943 Km/s
