Escape velocity? Point of no return?

[Baro]

I don't know much about space travel, but from talking to my friends playing this game it seems no matter how far out you get, you always end up falling back home. What does it take to totally leave the planet behind and be lost in space forever?

[Pyromaniac605]

To know that we'd have to know a few details about the planet, which AFAIK, HervesteR is still keeping secret.

[EatThePath]

A secret, but a discoverable one! A friend of mine took data points from one of my orbit and worked out the planet's mass from there. It's only one orbit, and perigee is grazing the atmosphere at that(43700m), but apparently the math works out well enough. According to him surface escape velocity is 3.431 km/s, and at 100 km altitude i' goes down to 3.176 km/s. The planet itself masses around about 5.29e22 kg

[kayweb]

Hit those figures just now, I'm not sure what's going to happen, because it is still deccelerating.

[cjameshuff]

A secret, but a discoverable one! A friend of mine took data points from one of my orbit and worked out the planet's mass from there. It's only one orbit, and perigee is grazing the atmosphere at that(43700m), but apparently the math works out well enough. According to him surface escape velocity is 3.431 km/s, and at 100 km altitude i' goes down to 3.176 km/s. The planet itself masses around about 5.29e22 kg

After doing some number crunching from that result to work out the proper velocities for circular orbits at various altitudes, I successfully entered a orbit with perigee of 228.089 km and apogee of 258.997 km, 2009 m/s and 2083.9 m/s respectively (eccentricity 0.06). I reran the numbers with my own orbit and got 5.29e22 kg again.

For comparison, our moon masses 7.3477e22 kg. It is of course much larger and lower density, giving it a much lower surface gravity...the planet of the Kerbals has a radius of only 600 km, and a surface gravity of 9.807 m/s^2, same as ours (standard gravity: 9.80665 m/s^2), which gives an easier way to calculate the mass. The overall density of the world is 7.4 times that of iron, 2.6 times that of iridium. (http://www.wolframalpha.com/input/?i=5.29e22+kg%2F%284*pi*%28600+km%29%5E3%2F3%29)

[HarvesteR]

Yeah, the planet is insanely dense

This little departure from realism is because the planet must be smaller than Earth, so as to make orbiting a more dynamic and fun experience, but the force of gravity must 'feel' earthly, so that means the planet needs to be very very massive and dense to make that happen.

5.29e22 is pretty close, I recall someone else did the same calculations, and came up with a very similar number. Interestingly enough, this number doesn't figure at all on the gravity model. Gravity is calculated starting from a G-at-surface value, which is then converted to a G-at-center value based on the square of the distance, so the mass of the planet is cancelled out of those equations.

The idea behind this is that it's possible to very easily tweak the gravity values of planets, and also achieve non-realistic, but possibly very fun scenarios.

Cheers

[Icefox]

Hit those figures just now, I'm not sure what's going to happen, because it is still deccelerating.

If you hit escape velocity exactly, then you will constantly decelerate toward 0 m/s but never actually reach it... no matter how far from the planet you are, you will always be moving away at least a little bit. (Technically you would hit 0 at infinite distance.) So if you hit escape velocity + 100 m/s, you will slowly decelerate all the time but never go below 100 m/s.

[cjameshuff]

This little departure from realism is because the planet must be smaller than Earth, so as to make orbiting a more dynamic and fun experience, but the force of gravity must 'feel' earthly, so that means the planet needs to be very very massive and dense to make that happen.

Given that the fastest stable orbits around Earth take about 90 minutes, scaling things down definitely makes sense. You could speed things up instead, but manually controlled launches would become unworkable without varying the simulation speed. (And it looks like orbit periods get up to 90 minutes at around 800 km altitude, 24 hours at 8150 km.)

Simulations used for planning real trajectories also don't generally use planetary masses, they use G*M, the product of the gravitational constant and the planetary mass. This is because the value of G*M can be measured directly, more precisely than G itself has been measured, and the values used for planetary masses and G would both have to be revised whenever G is measured to greater precision.

Anyway, I generated a table of escape velocities and circular orbit velocities:

https://gist.github.com/1073201

If you're moving at less than escape velocity at your given altitude, you're either in orbit or on a trajectory that'll hit something.

[AndrewCoja]

Would you be able make a calculator of sorts to would let someone find what exact velocity they need at any given height? Or say what equation you used so I can make my own?

[C3PO]

Escape velocity is generally calculated at periapsis, and it's the horizontal speed. You can never reach escape velocity vertically. As long as there's only one gravity field, you'll fall back down eventually.

But if you get high enough, even a small angle from vertical will have enough tangential speed to make you escape.

[Skumby]

Anyway, I generated a table of escape velocities and circular orbit velocities:

https://gist.github.com/1073201

Any chance you could give the orbit velocities for some of the lower orbits? Every 5 or 10 km from 35km to 100 would be great. Any higher and you can take a nap between orbits

[cjameshuff]

Escape velocity is generally calculated at periapsis, and it's the horizontal speed. You can never reach escape velocity vertically. As long as there's only one gravity field, you'll fall back down eventually.

But if you get high enough, even a small angle from vertical will have enough tangential speed to make you escape.

Escape velocity is for any direction that doesn't intersect the body being escaped (or atmosphere). A perfectly radial trajectory will still escape, even if that's the only other body in the universe. It's just a matter of having kinetic energy + gravitational potential energy > 0, so you have kinetic energy left over after climbing all the way out of the gravity well.

[cjameshuff]

Any chance you could give the orbit velocities for some of the lower orbits? Every 5 or 10 km from 35km to 100 would be great. Any higher and you can take a nap between orbits

If you get much below 40 km, drag seems to become quite significant. You're also not saving much time...a surface-level orbit, if it were possible, would be 26 minutes, compared to 29 for 50 km.

[cjameshuff]

Would you be able make a calculator of sorts to would let someone find what exact velocity they need at any given height? Or say what equation you used so I can make my own?

I've put some Ruby scripts on GitHub:

https://github.com/cjameshuff/rbkerbal

kerbalorbit.rb is such a calculator:

Exocortex:rbkerbal/% ./kerbalorbit.rb 60000               
r: 660000 km
Escape velocity = 3270.63 m/s
Circular orbit: velocity = 2312.68 m/s, period =  29.89 min
Apogee of transfer orbit to 30 km altitude: velocity = 2285.63 m/s, half-period =  14.44 min

[cjameshuff]

And here's another table of circular orbit velocities and periods and escape velocities every 5 km up to 995 km:

https://gist.github.com/1075144

[Sordid]

I've put some Ruby scripts on GitHub:

https://github.com/cjameshuff/rbkerbal

kerbalorbit.rb is such a calculator:

Exocortex:rbkerbal/% ./kerbalorbit.rb 60000               
r: 660000 km
Escape velocity = 3270.63 m/s
Circular orbit: velocity = 2312.68 m/s, period =  29.89 min
Apogee of transfer orbit to 30 km altitude: velocity = 2285.63 m/s, half-period =  14.44 min

Another option:

Copypaste this: ?((6.67x10^-11x5.29x10^22)/600000)

Put it into this: http://www.wolframalpha.com/

Replace 600000 by your desired altitude in meters; 600000 is sea level, since the radius of the planet is 600 km, 640000 is the edge of the atmosphere.

[memy]

If the diameter is 600km, wouldn't sea level be 300km?

[cjameshuff]

If the diameter is 600km, wouldn't sea level be 300km?

It would be, but the diameter's 1200 km.

[Sordid]

Yeah, confusing diameter with radius. Sheesh. *slaps self*

Corrected.

[rutsber]

Hey Sordid, haven't I seen you before?

Also, if you get to about 250,000 km out and are still going 18000 or so m/s, I don't think there is much that is going to bring you back.