Question

Isaac newtons theory of universal gravitation states that the equation F=G m^1m^2/r^2 can be used to calculate the amount of gravitational forces in newtons between 2 point masses (m^1) and (m^2) separated by a distance (r). G is a constant equal to 6.67*10^-11 m^2 kg^-2. The mass of the earth m^1 is equal to 5.97*10^24 kg, the mass of the moon m^2 is equal to 7.36*10^22 kg, and the distance r between the two is 384,000,000 m.
a. Express the distance r in scientific notation

b. Compute the amount of gravitational force between the earth and the moon. Express the answer in scientific notation.

Answer 1

The distance (r) on scientific notation= 3.84 × 10^8m

The amount of gravitational force between the earth and the moon = 1.9× 10^20N

Calculation of gravitational force

Tue formula that can be used to determine the gravitational force according to Issac Newton,

F = G m^1m^2/r^2

Where, G = 6.67*10^-11 m^2 kg^-2.

M1 = 5.97*10^24 kg

M2 = 7.36*10^22 kg

r = 384,000,000 m (which is = 3.84 × 10^8m in scientific notation).

Therefore F= 6.67*10^-11 (5.97*10^24×7.36*10^22)/3.84 × 10^8²

F= 6.67×10^-11 × 43.93×10^46/3.84 × 10^8²

F= 293.01× 10^35/3.84 × 10^8²

F= 293.01× 10^35/ 1.4745×10^17

F= 1.9× 10^20N

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