Spacecraft splitting into two near a planet

[Noakhailla Hola]

Homework Statement

I am doing a MATLAB simulation for a spacecraft that splits into two near a planet, and one part enters the planet's orbit while the other part avoids the orbit. I am a bit unsure about the physics of the split. Since there is a net force due to gravity, I guess momentum is not conserved. Given only the initial velocity of the whole spacecraft , how do I know what velocities the separated pieces will have immediately after the split?

Homework Equations

The Attempt at a Solution

 

[BvU]

Hello Noakhailla,

PF culture and guidelines require some more effort on your part. In fact I'm not really allowed to help at this point, but I'll honour your correct observation

Since there is a net force due to gravity, I guess momentum is not conserved

True. But think about the nature of this force: it's a central force, so maybe you can do something with angular momentum...
The scenario mentions one part in orbit which you may assume to be circular. The other not. A useful concept re orbit maneuvers is delta-v.

 

[Noakhailla Hola]

Hey BvU,

Thank you so much for your reply, and I am extremely sorry for not following the guidelines. I will definitely do that next time. To be specific, when the spacecraft gets near the planet, it will just split without really a thrust or anything. The two parts will have different mass. The bottom part will have more mass, so I was thinking it would curl under the influence of gravit y more than the lighter part. I was hoping to set the masses just right so that the heavier part falls into orbit while the lighter part just misses the orbit. The heavier part would also use the planet's atmospheric friction in the process of falling into orbit (aerobraking). I am just unsure of what would happen right after the split. If the whole spacecraft has mass 5 kg, heavier part has mass 4 kg, lighter part has mass 1 kg, and velocity of whole spacecraft is 10 m/s before the split, then what would be the velocities of the two parts after the split? I have attached a picture of a potential situation where the whole spacecraft is near the planet. The red circle is the planet, and the blue circle is the spacecraft before splitting.

 

[BvU]

It seems to me you are doing this as a programming exercise more than as a physics exercise, but I may be too pessimistic .
Do the links I gave mean anything to you or are they gibberish ? Angular momentum, delta-v etc. ?
Is it clear what you need for an orbit (a circular orbit is complicated enough for a start) ?

it will just split without really a thrust or anything

Can't do. No thrust (or at least some pushing apart), no split.
The splitting process conserves momentum in the center of mass system of the spacecraft (Newton 3) and is the only opportunity to influence velocity vectors in the planet coordinate frame (without wasting costly propellant). The requirement 'falling into orbit' of one fraction then leaves the other part with a specific velocity that dictates a trajectory. Can you simulate all that ?

You bring in aerobraking, which is an extra complication -- maybe it's good to play out the situation without aerobraking first: landing on the moon, for instance. You can't use the aerobraking for 'falling into orbit' because it doesn't switch off, so the object would 'fall out of orbit' straight away.

There are a bunch of variables that are pretty important in this scenario and that play a role in the time development. I can see two lines of code only.

 

[Janus]

Hey BvU,

Thank you so much for your reply, and I am extremely sorry for not following the guidelines. I will definitely do that next time. To be specific, when the spacecraft gets near the planet, it will just split without really a thrust or anything. The two parts will have different mass. The bottom part will have more mass, so I was thinking it would curl under the influence of gravit y more than the lighter part. I was hoping to set the masses just right so that the heavier part falls into orbit while the lighter part just misses the orbit. The heavier part would also use the planet's atmospheric friction in the process of falling into orbit (aerobraking). I am just unsure of what would happen right after the split. If the whole spacecraft has mass 5 kg, heavier part has mass 4 kg, lighter part has mass 1 kg, and velocity of whole spacecraft is 10 m/s before the split, then what would be the velocities of the two parts after the split? I have attached a picture of a potential situation where the whole spacecraft is near the planet. The red circle is the planet, and the blue circle is the spacecraft before splitting.

Just splitting the spacecraft into two unequal masses will not cause the two parts to follow different trajectories. When you are dealing with a relative mass ratio like you get between a spacecraft and a planet, the mass of the spaceship (or its separate parts) has no effect on the orbital trajectory. ( a 1 ton object orbiting at a given distance will have the same orbit and orbital velocity as a 100 ton object orbiting at that same distance. The reason for this is that even though the more massive object is attracted to the Earth by a greater force, it also has an equally greater momentum and it takes a greater force to curve its path by an equal amount as the less massive object. The effect of the increase in gravitational mass is canceled out by effect of the increase in inertial mass.

The only way to make them follow different trajectories is for for you to apply an additional force to one or the other by firing engines or something along those lines. (if you are close enough to the planet and split the ship into lower and upper sections, tidal forces will slowly separate the two halves. However, for something the size of a spaceship, tidal force will be extremely weak, the process excruciatingly slow, and it still won't be sufficient to put one half in orbit while the other escapes orbit.)

 

[CWatters]

Perhaps start by understanding what the conditions are for part remaining in orbit. Basically that part has to end up at the right altitude an velocity.

It's not hard to imagine the spacecraft arriving at the correct altitude but too fast. Then when the split occurs one part gains speed and the other looses speed and is left behind in orbit.

The maths should be quite easy for that scenario.