The formula to calculate the Delta-v (Δv) for a Hohmann Transfer is:
\[ \Delta v = \sqrt{\mu \left( \frac{2}{r1} - \frac{1}{a} \right)} \]
Where:
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.
Consider an example where:
Using the formula to calculate the Delta-v:
\[ \Delta v = \sqrt{398600 \left( \frac{2}{7000} - \frac{1}{14000} \right)} = \sqrt{398600 \left( 0.0002857 - 0.0000714 \right)} = \sqrt{398600 \times 0.0002143} = \sqrt{85.428} \approx 9.24 \text{ km/s} \]
This means that the delta-v required for this example is approximately 9.24 km/s.