When does surface gravity stop?

[gc1ceo]

I'm doing some math and I'm curious if surface gravity suddenly stops or if it slopes out in terms of calculating TWR from Mass?

The simplistic nature of KSP would seem to suggest that once you have cleared the atmosphere it is effectively zero for TWR calculations but I wanted to get some second opinions just to be on the safe side.

[Streetwind]

Once you are in orbit, the orbit itself nullifies gravity and you are weightless... provided you thrust exactly prograde, retrograde, normal or antinormal. If you thrust in relation to the center of gravity of the orbited object, then you will still be fighting gravity.

As for when gravity stops: that's what the "Sphere of Influence" is. KSP uses a simplified gravity model called "patched conics" in which you are only ever affected by the gravity of one single object at a time. Everytime you change into a different sphere of influence, you become affected by a different source of gravity. Going from Kerbin's SoI into that of the Mun means Kerbin's gravity ceases to exist for you and that of the Mun starts existing.

[Taki117]

Surface Gravity is constant at all altitudes within the SOI of the body you are orbiting so your TWR will be the same.

[Streetwind]

Constant? Nope. Influence of gravity decreases over distance. Quite a bit, in fact. I think it's quadratic or something similar.

You can easily see that with objects in highly eccentric orbits. Almost all the acceleration from falling towards the periapsis comes in the last few percent of the way.

[mhoram]

TWR is simply the ratio between thrust and weight with the formula

TWR = F_thrust / (mass * g)

So you have to decide what kind of TWR you want to calculate.

For a TWR based on surface gravity, g never changes.

For a TWR based on current gravity, you can calculate g as g = Planets_Gravitational_parameter / distance^2

And the gravity of a planet, moon or sun is always in effect while you are within its Sphere of Influence (SOI).

Most of the references to TWR however you will find here on the forum are based on the surface gravity of Kerbin.

Edited January 19, 2014 by mhoram

[Silverchain]

You are always under the effect of the gravity of one body, that's the only major simplification in KSP.

In vacuum, with engines off, your ship would keep going in a straight line. Gravity pulls it down towards the planet (or moon, or sun). When the pull of gravity downwards is enough to keep bending the path of your ship around the planet, you're in orbit.

Gravity at a given radius is given by F = GMm / r^2.

G is the gravitational constant. M is the mass of the large body. m can be set equal to 1kg and conveniently removed. r is the radius from the centre of the large body.

For Kerbin its equatorial radius is r = 600000. Its mass is 5.29 * 10^22 kg. G is equal to 6.67 * 10^-11 thingummys.

Which gives Kerbin surface gravity = 6.67 * 10^-11 * 5.29 * 10^22 / (6 * 10^5)^2

= 6.67 * 5.29 * 10^11 / (36 * 10^10)

= 35.28 * 10 / 36

~ 9.8 ms-2

Which is what you'd expect.

For a spacecraft in a 100km altitude orbit, the new radius is 600km (Kerbin's radius) + 100km (the height) = 700km.

Plug the numbers into the equation and we get:

~ 7.2 ms-2

At 200km, the radius is 800km...

~5.5 ms-2

At 1000km, the radius is 1600km...

~2.7 ms-2

And so on, until we reach a point a long way out where the game decides that the Sun's influence is more important than Kerbin's, and calculations are made relative to the Sun instead of relative to Kerbin.

Basically, if you use your engines to come to a dead stop in space at some point near Kerbin, this is how strong gravity will be at a given height.