Impacts! The relative velocity of an Asteroid impacting Earth depends on the dir

Question

Impacts! The relative velocity of an Asteroid impacting Earth depends on the direction it is approaching Earth’s orbit from.

a. Earth’s escape velocity is ~11 km/s, the Earth orbits the sun at ~30 km/s, and an asteroid crossing Earth’s orbit would have about the same velocity of ~30 km/s. What are the minimum and maximum velocities of impact for an asteroid hitting Earth?

b. Asteroid 1 with mass m1 hits Earth at a velocity of v1 = 50 km/s. Asteroid 2 with mass m2 = 2m1 hits Earth at a velocity v2 = 25 km/s. Which asteroid forms a bigger crater? Why?

Explanation / Answer

a) The minimum speed for an asteroid is achieved if it has more or less the same velocity around the Sun as the Earth. It means in this case it will atleast have a velocity of 11 m/s which is also equal to the escape velocity of earth.

Earth speed around sun is 30 km/s. So if we compare escape velocity of earth and it's orbital speed then we can see,

meteor will have a speed of sqrt(2) * 30 = 42 km/s . Therefore, maximum impact velocity will be

30 km/s + 42 km/s = 72 km/s

b) The kinetic energy of first meteor is given as K.E = 1250m1

for second , K.E = 625m1 . It is obvious that K.E for first is more for given mass m1, so it will form bigger crater.

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