Astronomers detect a distant meteoroid moving along a straight line that, if ext

Question

Astronomers detect a distant meteoroid moving along a straight line that, if extended, would pass at a distance 3RE from the center of the Earth, where RE is the Earth's radius. What minimum speed must the meteoroid have if it is not to collide with the Earth? (Assume the meteorite is detected when it is very far from the Earth. Use any variable or symbol stated above along with the following as necessary: G for the gravitational constant and ME for the mass of the Earth.)

v= ____________________

Explanation / Answer

the asteroid should have minimum velocity so that the total energy at the minimum approach point is zero.

if the total energy is less than zero the asteroid would collide with the earth.


=> G*Me*m/3Re = 1/2*m*v^2

=> v = sqrt ( 2*G*Me/3Re)

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