Two meteoroids cross the moons orbit (the radius of the moons orbit is 3.84 x10^

Question

Two meteoroids cross the moons orbit (the radius of the moons orbit is 3.84 x10^8m) moving at 2.0 km/s.

a) One of the meteoroids is heading straight for earth. Use conservation of energy to find the speed at which it hits the earths surface. Hint: the radius of the earth is given by RE = 6.37 x 10^6m and the mass of the earth is ME = 5.97 x 10^24 kg. Also, be sure to convert km/s to m/s when calculating the KE.

b) The other meteoroid is heading directly away from earth. Find the total energy of the meteoroid and determine whether it escapes the earth or not. If it escapes, find its velocity when it is far from the earth. If it doesnt escape, find the maximum distance from the earths center reached by the meteoroid.

Explanation / Answer

a)Conserving energy,

-GMm/r1+0.5mu^2=-GMm/r2+0.5mv^2

6.67*10^-11*5.97*10^24*(1/6370000-1/384000000)+0.5*2000^2=0.5*v^2

v=11267m/s

b)If total energy initially is greater than 0, it will escape.

-GMm/r1+0.5mu^2=-6.67*10^-11*5.97*10^24/384000000m+0.5*m*2000^2=963023m

Since it is positive, it will escape.

Conserving energy again,

-GMm/r1+0.5mu^2=0.5mv^2

0.5v^2=963023

v=1387.8m/s

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