Answer:
Part (i) the force of attraction between Mars and the satellite is 965.78 N
Part (ii) the speed of the satellite in a perfectly circular orbit 2016.99 m/s
Part(iii) time it takes the satellite to complete one revolution is 32809.78 s
Part (iv) the radius of the orbit
Part (v) the radius of the orbit is 8.425 x 10⁷ m
Explanation:
Part (i) the force of attraction between Mars and the satellite
Given;
mass of Mars, m₁= 6.4191 x 10²³ kg
mass of satellite, m₂ = 2500 kg
Distance between the satellite and Mars, R = radius of mass + 2.1 times the radius of Mars = 3.397 x 10⁶ m + 2.1(3.397 x 10⁶ m) = 1.0531 X 10⁷ m
Where;
G is gravitational constant = 6.67428 x 10⁻¹¹ Nm²/kg²
Part (ii) the speed of the satellite in a perfectly circular orbit
According to Newton's second law;
F = ma and a = v²/R
Part(iii) time it takes the satellite to complete one revolution
one complete revolution = 2πR
= 2π X 1.0531 X 10⁷ m = 6.6177 X 10⁷ m
Part (iv)
From the formula above, it is the mass of Mars and Radius of orbit.
Thus, the correct answer is the radius of the orbit
Part (v)
If it takes 8 times longer, T = 8 X32809.78 s = 262478.24 s
D = T*V
= 262478.24* 2016.99 = 529415985.3 m
D = 2πR
R = D/2π
= (529415985.3)/2π
= 8.425 x 10⁷ m