Your job with NASA is to monitor satellite orbits. One day, during a routine survey,
you find that a 400 kg satellite is going to collide with a smaller 100 kg satellite travelling in the same
orbit but in the opposite direction. Knowing the construction of the two satellites you expect they will
become enmeshed into a single piece of space junk. When you notify your boss of the impending
collision, he asks you to quickly determine whether the space junk will continue to orbit or crash into
Earth.

my work so far....

(Msat • v2) / R = (G • Msat • MCentral ) / R2


Where Mcentral is Mearth
I'm completely lost after this... im not sure where im headed either, I would be eternally grateful if someone could outline what is needed here... thanks!

Basically we have to determine whether the velocity of the space junk created after collision is sufficient to continue in a circular orbit around the earth, or whether the velocity of the junk is such that the junk follows a different trajectory to crash into the earth.


So the combined mass of the junk m = m1+m2 = 500kg (sum of the individual masses of the two satellites)

Now, Orbital velocity for this "object" of mass m would be = sqrt(MG/R) where R is the radius of orbit of the satellites.

So find the velocity of the junk after collison.


EDIT: we find the velocity of the junk by applying linear momentum conservation laws since the collision is inelastic and will surely involve KE losses.

Hence, applying conservation of momentum, we obtain the value of the new velocity as (2/3)Vo where Vo is the orbital velocity sqrt(GM/R).

Hence, the junk takes an elliptical trajectory with a possibility of collison with the earth.

(Conclusive result will only be obtained when we actually derive the equation of trajectory of the junk.)

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Just another brick in the wall...

thanks for the edit, akshay. this is matching with my results.
actually i found 1 data is missing, do u think we can do it by just using total E <0 for elliptic orbits?
i could not guarantee it will hit.
it can still hover around in a lower orbit.what do u think?

[/quote]it can still hover around in a lower orbit.what do u think?[/quote]

Exactly my point. It could still move in an inner ellipse without colliding. Or the elliptical trajectory maybe such that it crashes into the earth at some point in its motion.

__________________
Just another brick in the wall...