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7 August, 09:18

It is observed that the number of asteroids (or meteoroids) of a given diameter is roughly inversely proportional to the square of the diameter.

Part A

Assuming a density of 3000 kg/m3 and approximating the actual distribution of asteroids and meteoroids as a single 1000-km body (Ceres), one hundred 100-km bodies, 10 thousand 10-kmbodies, and so on, calculate the total mass in the form of 1000-km bodies.

Part B

Calculate the total mass in the form of 100-km bodies.

Part C

Calculate the total mass in the form of 10-km bodies.

Part D

Calculate the total mass in the form of 1-km bodies.

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Answers (1)
  1. 7 August, 11:25
    0
    (a) M = = 1.57 * 10²¹kg

    (b) M = = 1.57 * 10²⁰kg

    (c) M = = 1.57 * 10¹⁹kg

    (d) M = = 1.57 * 10¹⁸kg

    Explanation:

    (a) For 1000km body, diameter D = 1000km = 1,000,000 m

    and N = (1000/D) ² = (1000/1000km) ² = 1

    substituting into the formula, we have

    M = 1 * 4/3 π*3000*[1000000/2]³

    =1.57 * 10²¹kg

    (b) For 100km body, diameter D = 100km = 100,000 m

    and N = (1000/D) ² = (1000/100km) ² = 100

    substituting into the formula, we have

    M = 1 * 4/3 π*3000*[100000/2]³

    =1.57 * 10²⁰kg

    (C) For 10km body, diameter D = 10km = 10,000 m

    and N = (1000/D) ² = (1000/10km) ² = 100

    substituting into the formula, we have

    M = 1 * 4/3 π*3000*[10000/2]³

    =1.57 * 10¹⁹kg

    (C) For 1km body, diameter D = 1km = 1,000 m

    and N = (1000/D) ² = (1000/1km) ² = 100

    substituting into the formula, we have

    M = 1 * 4/3 π*3000*[1000/2]³

    =1.57 * 10¹⁸kg
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