Answer: 4.486N
Explanation:
The Gravitational force of attraction 'F' between two masses m1 and m2 is given by:
F= Gm1m2 / r^2
Where ; r = distance between the bodies
G = gravitational constant = 6.67 × 10^-11
The mass of the earth (m1) = 5.98 × 10^24 kg
Mass of the moon (m2) = 7.35 × 10^22 kg
Mass of rocket (m3) = 1200 kg
the net gravitational force on the rocket from the earth and moon equals
Difference in the gravitational force between the earth and rocket and that exerted between th e moon and rocket.
Net F = (Gm1m3 / r^2) - (Gm2m3) /r^2
Net F = Fa - Fb
Fa = Gm1m3 / r^2 =
(6.67 × 10^-11 × 5.98 × 10^24 × 1200) /(3 × 10^8)^2
(6.67×5.8×1200)/ 9 × 10^(-11 + 24 - 16)
= 5318 × 10^-3 = 5.32N
Fb = Gm2m3 / r^2 =
r = (3.84 × 10^8 - 3.0×10^8) = 0.84 × 10^8
(6.67 × 10^-11 × 7.35 × 10^22 × 1200) /(8.4× 10^7)^2
(6.67×7.35×1.2)/ 70.56 × 10^(-11 + 22 + 3 - 14)
= 0.83375N
Fnet = 5.32N - 0.83375N = 4.48625N
= 4.486N
