Exercise 10.48 Suppose that an asteroid traveling straight toward the center of

Question

Exercise 10.48

Suppose that an asteroid traveling straight toward the center of the earth were to collide with our planet at the equator and bury itself just below the surface.

Part A

What would have to be the mass of this asteroid, in terms of the earth's mass M , for the day to become 26.0% longer than it presently is as a result of the collision? Assume that the asteroid is very small compared to the earth and that the earth is uniform throughout.

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Exercise 10.48

Suppose that an asteroid traveling straight toward the center of the earth were to collide with our planet at the equator and bury itself just below the surface.

Part A

What would have to be the mass of this asteroid, in terms of the earth's mass M , for the day to become 26.0% longer than it presently is as a result of the collision? Assume that the asteroid is very small compared to the earth and that the earth is uniform throughout.

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Incorrect; Try Again; 3 attempts remaining

Explanation / Answer

tinme period of earth T1 = 24 hrs

T2 = 26% of T1 + T1 = 24* 0.26 + 24 = 30.24 hrs

now use use Keplers third as T^2 = 4pi^2 R^3/GM

where M is mass of the Jupiter

G s Universal gravitationa constant

so T^2 is inversly proportional to M

T2^2/ T1^2 = M1/M2

M2/M1 = (T1/T2)^2

M2/M1 = 24/30.24)^2

M2 = 0.63 times the mass of earth

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