Tilted large deviation principle

Template:Orphan Gate orbits are optimal circular departure orbits for transfer from one planet to another. At certain specific orbits around a cosmic body, the additional delta-v required to go from orbital velocity to hyperbolic trajectory for an interplanetary transfer, is minimal. Gate orbits can therefore be very useful for minimising the delta-v budget for an interplanetary trip.

For example, the required delta-v for a Hohmann transfer orbit from the Earth to Mars (considering Earth at 1 AU and Mars at 1.52 AU) is 2.94 km/s. To reach 2.94 km/s at infinity from a low Earth orbit at, say 200 km altitude, requires a 3.61 km/s burn. If the vehicle were to leave the Earth's attraction from the 92,000 km high Mars gate orbit instead, required delta-v would be only 2.08 km/s. At higher still orbits the required delta-v rises again. For example, at 150,000 km, required delta-v is now 2.17 km/s.

Reducing the delta-v from 3.61 to 2.08 km/s can reduce the total mass of the vehicle by as much as 38%, or increase the payload by 62%!

The radius of a given gate orbit can be calculated using the following equation:

$r=\frac{2\mu }{v_{\mathrm{\infty }}^2}$

where:

• $r$ is the distance between the orbiting body and the central body, in km
• $\mu$ is the standard gravitational parameter, in km³s⁻²
• $v_{\mathrm{\infty }}$ is the required velocity at infinity, in km·s⁻¹. Remember $v_{\mathrm{\infty }}^2$ is also known as $C3$

External links

• Interplanetary Gate Orbits by Marco Christov