A basic orbital mechanics question

[nhnifong]

If you know how much mass a launcher can put in LEO, Do you have enough information to determine how much mass it can put in GTO, or a Lunar or Martian trasfer orbit? What are the coefficients that relate these quantities?

[MockKnizzle]

Really all you need for that kind of calculation is the rocket equation. You can pretty easily find/approximate the necessary dV for those transfers, and just plug that additional dV into the rocket equation and solve for payload mass.

If you're looking for a quick rule-of-thumb, I have no idea

[magnemoe]

Its usually listed for most rockets at least to LEO and GEO, however it depend a lot of the design.

Ariane has an much higher GEO versus LEO ratio than falcon 9 because its uses H2+O2 in upper stage and have an small upper stage and boosters rather than two stages and a larger second stage like falcon 9.

[metaphor]

It depends on the Isp and mass fraction of the upper stage(s). The delta-v for GTO is about 2.4 km/s from LEO, lunar transfer is about 3.2 km/s, Mars transfer (with inclination change) is about 3.6-4 km/s. With the usual hydrolox upper stage you can usually get about 1/2 of your LEO payload to GTO, 1/2.5 of your LEO payload to TLI, and 1/3 of your LEO payload to TMI. With kerolox it's more like 1/3, 1/4, 1/5.

edit: GTO, not GEO

Edited October 5, 2014 by metaphor

[nhnifong]

Thank you metaphor!

[Idobox]

Its usually listed for most rockets at least to LEO and GEO, however it depend a lot of the design.

Ariane has an much higher GEO versus LEO ratio than falcon 9 because its uses H2+O2 in upper stage and have an small upper stage and boosters rather than two stages and a larger second stage like falcon 9.

What is usually given is the GEO insertion. The payload has to circularize by itself, as the upper stage will fall back to Earth. The fuel requirements to circularize when you're already on an insertion orbit isn't huge, but it still matters.