Estimate the average distance between asteroids that reside between th

1.	Estimate the average distance between asteroids that reside between the orbits of Mars and Jupiter. Total area = 1.74 x 1018 km2. Assume that this area is populated by 2 × 106 individual asteroids and that the area surrounding each asteroid is circular in shape.
Answer» Area surrounding each asteroid (A) A((1.74 x 10¹⁸)/(2 x 10⁶)) = 0.87 x 10¹²km² Radius of the area (A) A = r²π, r = (A/π)^1/2 r = ((0.87 x 10¹²)/3.14)^1/2 = (0.2770 x 10¹²)^1/2 = 0.526 x 10⁶km r = 526, 000km

Estimate the average distance between asteroids that reside between the orbits of Mars and Jupiter. Total area = 1.74 x 1018 km2. Assume that this area is populated by 2 × 106 individual asteroids and that the area surrounding each asteroid is circular in shape.

Answer»

Area surrounding each asteroid (A)

A((1.74 x 10¹⁸)/(2 x 10⁶)) = 0.87 x 10¹²km²

Radius of the area (A)

A = r²π, r = (A/π)^1/2

r = ((0.87 x 10¹²)/3.14)^1/2 = (0.2770 x 10¹²)^1/2 = 0.526 x 10⁶km

r = 526, 000km