The rocket equation: Help!

[Drunkrobot]

I'm sure most of you are aware of this equation:

http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation

Effective exhaust velocity is equal to specific impulse multiplied by acceleration due to gravity.

However, all the examples of the equation I have seen takes gravity (F_g) to be 9.81, the gravity on Earth (or Kerbin) at sea level.

While I know that it won't be 9.81 on the Moon, for example (My probe on the Mun reads 1.6 m/s²), I what to know if it is true at an altitude in the SOI of Earth (or Kerbin).

I want to know because I'm trying to design a transfer stage on my Mun rocket with the minimum fuel needed. Do I use 9.81 to equal F_g, or 7.78 (the gravity my probe in a 70 km orbit reads.) Thanks!

Edited July 17, 2013 by Drunkrobot
Answered!

[Mr Shifty]

However, all the examples of the equation I have seen takes gravity (F_g) to be 9.81, the gravity on Earth (or Kerbin) at sea level.

For specific impulse, g is just a constant of proportionality that, by convention, is taken to be the acceleration due to gravity at the Earth's surface. So for the rocket equation you always have to use 9.81, no matter where you are.

[capi3101]

Yeah, for the rocket equation, that's always going to be 9.81 regardless of where you are. Mun, Kerbin, Duna...makes no difference.

Where different gravity values come into play is when you're trying to figure out your thrust-to-weight ratios for your various stages - a rocket that has a TWR of 1.6 on Kerbin will have a much higher TWR on the Mun, and insanely high TWR on Gilly, an insufficiently low value on Eve and so forth.

[Frederf]

It's supposed to be "g-naught" or g with the little zero subscript. It's a simple conversion value that doesn't depend on the actual local gravity at all much like converting kmph to mph.

I seem to recall in KSP g-naught is 9.80000000000000000000000 but I'm not 100% confident.

[nyrath]

Actually, Captain Arbitrary discovered that for some odd reason the Kerbal physics engine uses 9.82 for g-naught.

http://pa.reddit.com/r/KerbalSpaceProgram/comments/1hrah5/whats_the_best_mod_for_highefficiency_highthrust/caxaqo2

[Johnno]

Standard gravity, or standard acceleration due to free fall, usually denoted by g_0 or g_n, is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is defined as precisely 9.80665 m/s2

Found linked on that wikipedia page.