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.

(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

a lot of it means it can be "burned" for energy and sold at one price. if it is scarce, the price will go up

that tool is called an altimeter which measures your altitude which can be used to tell which atmosphere you are currently in, including the stratosphere.

hope this ! : )