- #1
geoffrey159
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Homework Statement
A spaceship is sent to investigate a planet of mass M and radius R. While hanging motionless in space at distance 5R from the center of the planet, the ship fires an instrument package with speed v0 (at angle ##\theta## with the line passing through the spaceship and the center of the planet). The package has mass m, which is much smaller than the mass of the spaceship. For what angle ##\theta## will the package just graze the surface of the planet ?
Homework Equations
The Attempt at a Solution
The origin of the frame is located at the center of the planet.
In the system 'spaceship + package', the external torque is 0 because the forces acting on it are radial. So the angular momentum is conserved. Furthermore, the final velocity vector of the package has to be perpendicular to the position vector, otherwise the instrument package would crash on the planet, so:
##L_i = 0 + 5mRv_0\sin(\theta) = 5mRv_0\sin(\theta) ##
##L_f = 0 + mRv = mRv ##
and then ##\theta = \arcsin(\frac{v}{5v_0})##. But I feel it is not all because I'm not using the fact that m is a lot smaller than the mass of the spaceship ? Maybe ##v## has an expression but I don't see how to find it. Any idea ?