Estimate how much energy would be deposited into the Earth if it is hit by a one

Question

Estimate how much energy would be deposited into the Earth if it is hit by a one tonne meteor traveling on an orbit around the Sun with a semi-major axis of 20.0 A.U. Note: in order to hit the Earth this meteor can not be in a circular orbit. Consider two cases: At the point of impact (a) the meteor is traveling parallel and in the same direction as the Earth’s orbit and (b) the meteor is traveling parallel and in the opposite direction. The velocity of an orbiting body was given in Module 3(c). A tonne is 1000 kg, the kinetic energy is given by ! mass ! velocity2 , and the Earth’s orbital velocity is approximately 30.0 km/s. (Marks: 4) Note on this question – there is no need to get very elaborate in your calculations, looking in detail at collision dynamics you will have learned in a Physics course. Kinetic energy is not conserved. Momentum is conserved but the change in the Earth’s velocity is essentially zero as a result of the collision (because of the enormous difference in masses). You can safely deal with this by asking how much kinetic energy, in the frame of the Earth, is lost in the change in motion of

Explanation / Answer

In both the cases, the kinetic energy of the meteor will be deposited on the Earth.

The kinetic energy is given by:

K = 1/2 x m x v^2

Velocity of the satellite is given by:

v = sqrt(GM/R)

where, G -> gravitational constant

M -> mass of the Earth

R -> distance of the satellite from the Earth

so:

v = sqrt((6.67 x 10^-11)(5.98 x 10^24)/(20 x 1.496 x 10^11 m) [since 1AU = 1.596 x 10^11 m]

= 11.55 m/s

So,

K = (1/2) x (1000kg) x (11.55)^2 = 66,655.41 J

So, 66,655.41 J of energy will be deposited into the Earth.

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