On July 4, 2005, the NASA spacecraft Deep Impact fired aprojectile onto the surf

Question

On July 4, 2005, the NASA spacecraft Deep Impact fired aprojectile onto the surface of Comet Tempel 1. This comet is about9.0km across. Observations of surface debris released bythe impact showed that dust with a speed as low as 1.0 m/s was able to escape the comet.

1) Assuming a spherical shape, what is the mass of this comet?( The escape speed for an object at the surface of Earth is 11.2 km/s).

2) How far from the comet's center will this debris be when ithas lost 70% of its initial kinetic energy at the surface?

Explanation / Answer

Hello :) Neglecting other factors that could be involved but not given: a. M=vR^2/2G remember R=45 km or 4.5 x10^4 m v=1m/s This is derived by setting up: mv^2/2=GMm/R And solving for M. b. If it loses 90% KE then it will only have 10% left. Distance with initial kinetic energy on the surface was R=2GM/v^2 R= 4.5 x 10^4 m = radius of the comet The distance should be ten times that with 90% loss of KE: d=10 x (radius of comet)= 4.5x10^5 m This is derived by setting up : (.1)[initial KE]=GMm/r and solving for r r=2(10)GM/v^2=20GM/v^2=10(radius of comet) Debris mass doesn't matter since it cancels out anyways but its initial velocity does at 1m/s It would only lose all of it at some imaginary point at inifinity. When R=2GM/v^2 and v approaches zero then R approaches infinity. v therefore could never really be zero but keep getting closer and closer. Seen from reverse: An object from a point at 'infinity' will never go faster than the escape velocity of the object before they collide if their mutual gravity is all that is causing their motions. Hope this helps :) Have a nice day!!

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