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The most common delta V error

25 Feb 2014, 02:46 UTC
The most common delta V error
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Patching ConicsTime and time again I've watched people patch conics by using straight addition and ignoring the Oberth benefit. It is a very easy mistake to make. I'll give an example of this error for an earth to Mars delta V budget.At perihelion an earth to Mars Hohmann orbit is moving about 33 km/s. 3 km/s is needed to leave earth's 30 km/s heliocentric orbit and enter this transfer orbit. In a similar fashion it takes 2.5 km/s to leave Hohmann transfer and match velocities with Mars.But before we go from one heliocentric orbit to another, we need to escape the planet's gravity well. Earth's surface escape velocity is about 11 km/s. Mars' surface escape velocity is about 5 km/s.The novice will look at these 4 quantities and simply add them. 11 + 3 + 2.5 + 5 is 20.5. They'll tell you it takes about 20.5 km/s to get from earth's surface to Mars surface.But to accurately patch conics you need to use the hyperbolic orbit that takes you out of the planet's sphere of influence to a heliocentric orbit. Hyperbolic orbit speed is sqrt(Vescape2 + Vinfinity2). But what's Vinfinity? In this example it's the 3 km/s needed to ...

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