Answer:
(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
