Physics Question

[Cryova]

Just as a cool question, what would happen if you had a ship in Low Kerbin Orbit, then launch another ship to dock with it, but you dock with it when one ship is in Orbit and one is on a sub-orbital trajectory? What would happen?

[Slam_Jones]

Unless I'm very much mistaken (which is entirely possible), in order to dock, they have to match each other's orbits. Either they will both be in sub-orbit, or both in orbit. Either way, when they connect, it will be one or the other.

Unless you're trying to dock at very high (relative) speed? I don't see that ending well, though...

[Padishar]

A big bang would happen. A sub-orbital trajectory will be considerably slower than the orbiting vessel so the two ships will be moving quite fast relative to each other. Even if you could manage to dock , conservation of momentum will result in the combined vessel travelling at less than orbital velocity so it would require a boost to keep it in orbit.

[mikegarrison]

Unless I'm very much mistaken (which is entirely possible), in order to dock, they have to match each other's orbits.

This is correct. They have to be in the same place, going the same speed, in the same direction. So basically they have to be in the same orbit.

[mhoram]

they would crash.

When you are in an 75x75 km you travel at a speed of ~2287 m/s

When you are in a sub-orbital 75x0 km orbit you travel at 75km altitude ~2219 m/s

So the velocity-difference between the two vessels is ~68 m/s

For the calculation Vis-Viva is your friend. https://en.wikipedia.org/wiki/Vis-viva_equation

[mikegarrison]

Another interesting thing that is somewhat hidden in KSP by the SOI approximation -- when you, for instance, go into Munar orbit after transferring from Kerbin, look at how your ship is pointed relative to Kerbin (not Mun). You will see that getting into Munar orbit basically means you have to burn in a very similar orientation to what it would take to circularize your Kerbin orbit if the Mun were not there.

[Alshain]

The act of rendezvous results in matching orbits. It is 100% possible to get an encounter with a craft while suborbital, in fact it is much more efficient to do it that way, I do it that way all the time (and so did Gemini 6 for what it's worth). However, as you slow down to approach the craft you may not realize it, but you are establishing orbit.

[gogozerg]

Docking means same place and same speed vector. Same place and same speed means same orbit.

[Vanamonde]

Science question moved to the science subforum.

[Camacha]

Even if you were able to somehow attach the vehicles quickly to each other, the resulting energy would likely mean it would be on a suborbital trajectory. Want a cheap deal, lose both ships

[PB666]

they would crash.

When you are in an 75x75 km you travel at a speed of ~2287 m/s

When you are in a sub-orbital 75x0 km orbit you travel at 75km altitude ~2219 m/s

So the velocity-difference between the two vessels is ~68 m/s

For the calculation Vis-Viva is your friend. https://en.wikipedia.org/wiki/Vis-viva_equation

IOW, ouch.

[0111narwhalz]

Hypothetically, if you had a big enough spring, you could absorb the energy of the intercept. However, this would still probably knock your 'orbiter' out of orbit, unless said orbiter had a mass many times that of the suborbital vessel i. e. a 'roid. Now, you could have your orbiter on a carefully calculated eliptical orbit, and get slammed into a circular one by the projec--I mean ship. It might then slowly build back up to this orbit afterwards using an ion drive or something.

Also, it's worth noting that orbital velocity is calculated based upon center-of-mass, so in reality a 75x0 suborbit is actually a 675x600. This is usually where my nearly-SSTO planes end up. You're more likely to end up with something like a 100x675 from Kerbin's center on a steep suborbital arc. Your game will show this as a Pe of -500 because those numbers are from sea level.

Edited September 18, 2015 by 0111narwhalz

[Steel]

they would crash.

When you are in an 75x75 km you travel at a speed of ~2287 m/s

When you are in a sub-orbital 75x0 km orbit you travel at 75km altitude ~2219 m/s

So the velocity-difference between the two vessels is ~68 m/s

For the calculation Vis-Viva is your friend. https://en.wikipedia.org/wiki/Vis-viva_equation

(...)*Please Ignore

(Although the Vis-Viva equation doesn't work well with sub-orbital trajectories, as a)* truely sub-orbital trajectory is essentially a ballistic arc rather than an orbit with its periapsis at 0km (if you treat it as an ellipse like a normal orbit, its lowest point would be inside the planet). A 75km by 0 km path is actually an orbit with it's lowest point in atmosphere, not a sub-orbital trajectory.

So in reality a sub-orbital flight would be have a much greater velocity difference.

In theory you could have a sub-orbital trajectory where you have no velocity at 75km and thus have a velocity difference of ~2287 m/s!

Edited September 20, 2015 by Steel

[Gaarst]

Although the Vis-Viva equation doesn't work well with sub-orbital trajectories, as a truely sub-orbital trajectory is essentially a ballistic arc rather than an orbit with its periapsis at 0km (if you treat it as an ellipse like a normal orbit, its lowest point would be inside the planet). A 75km by 0 km path is actually an orbit with it's lowest point in atmosphere, not a sub-orbital trajectory.

So in reality a sub-orbital flight would be have a much greater velocity difference.

In theory you could have a sub-orbital trajectory where you have no velocity at 75km and thus have a velocity difference of ~2287 m/s!

The Vis-Viva equation doesn't care about whether or not your orbit is suborbital: the radius of the body is not used in the equation, and as for all Newtonian/Keplerian mechanics, all bodies are treated as points at their centre of mass.

So for a suborbital equation, just use your orbital values as they are relative to the centre of the planet: it doesn't matter if your periapsis is 675km, 600km or 10km (above centre). You'll just have to use semi-major axis and relative distance to centre of the planet.

The Vis-Viva equation works with any Keplerian orbit: elliptic, suborbital (which is included in elliptic), parabolic and hyperbolic.

[Steel]

My mistake, this is why I shouldn't post impulsively while low on sleep!

[peadar1987]

Not quite the same thing, but I did my Masters' Dissertation on a capture system in LEO for projectiles launched from the moon.

It used a rotating tether 100km long, so the tip velocity could be far greater than the orbital velocity. It then used a net at the end of the tether, held taut by rotating masses at the corners, to gently decelerate the projectile and capture it.

The dissertation itself isn't online, but the poster for it is here: http://userweb.eng.gla.ac.uk/MScPosters2012-13/Mech/MSc%20Mechanical%20Engineering/Capture%20and%20Release%20Mechanism%20for%20Motorised.....pdf (I suck at making posters, but the project itself was okay)

Anyway, no reason a similar system couldn't be made for a suborbital projectile.

Essentially, you would use the rotating tether to accelerate the payload from suborbital to orbital speeds (My project was designed for a delta-V of 2.1 km/s). This would lower the tether's periapsis, but if it was high enough, you could use electrodynamic tether propulsion to reboost the tether system after every capture, without expending propellant.