Answer:
a) 2.02 years
b) 8.1 x 10⁻⁸.
Explanation:
Time period of a rotating body T² is proportional to radius of orbit R³ So
T₁² / T₂² = R₁³ /R₂³ ( T₁ and R₁ is time period and radius of orbit of the earth .)
1² / T₂² =( 1/1.6)³
T₂ = 2.02 years.
Kinetic energy of an orbiting body = 1/2 m v₀² ( v₀ is orbital speed)
= 1/2 m x 2 g R = m x G m/R² X R= m² x G /R
Kinetic energy of asteroid K₁ / kinetic energy of earth K₂ =
(mass of asteroid/mass of earth)² x( radius of earth / radius of asteroid)
=( 3.6 x 10⁻⁴)² x 1/1.6 = 8.1 x 10⁻⁸ .
