Engineering:Gate orbit

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:

[math]\displaystyle{ r = {2\mu \over v_\infty^2} }[/math]

where:

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

External links

• Interplanetary Gate Orbits by Marco Christov