Imagine that one day astronomers discover an asteroid that is still a large dist
ID: 1780956 • Letter: I
Question
Imagine that one day astronomers discover an asteroid that is still a large distance away from us, but heading on a path that, if straight, would bring it within 3.3 × 10^8m of the Earth (about the orbit of the moon). The asteroid’s speed at the time of the discovery is 754 m s . At this point, the gravitational pull of the Earth on the asteroid is still negligible, but of course as it gets closer it will get pulled towards the Earth. Using the information given, and the radius of the Earth (6.37 × 10^6m), determine whether the asteroid will actually hit the Earth or not.
Explanation / Answer
escape speed is Ve = sqrt(2*G*M/R)
G is the universal gravitational constant
M is the mass of the earth
R is the orbit of earth
Ve = sqrt(2*6.67*10^-11*5.97*10^24/(6.37*10^6))= 11181.4 m/sec
using law of ocnservation of energy
energy at the moon's orbit = energy at the surface of earth
(0.5*m*v^2) = (0.5*m*v1^2)-(G*m*M/R)
m is the mass of the asteroid which cancels on both sides
(0.5*754^2) = (0.5*v1^2)-(6.67*10^-11*5.97*10^24/(6.37*10^6))
V1 = 11206.77 m/sec
since this speed of the asteroid at the surface of earth is greater than escape speed so the asteroid cannot hit the earth