The earth has a mass of 5.98 × 10^24 kg and the moon has a mass of 7.35 × 10^22 kg. The distance from the centre of the moon to the centre of the earth is 3.84 × 10^8 m. A rocket with a total mass of 1200 kg is 3.0 × 10^8 m from the centre of the earth and directly in between the earth and the moon. Find the net gravitational force on the rocket from the earth and moon.

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