Question

Problem 6.41 - Enhanced - with Feedback. The mass of the sun is 1.99×1030kg and its distance to the Earth is 1.50×1011m . What is the gravitational force of the sun on the earth?The mass of the moon is 7.36×1022kg and its distance to the Earth is 3.84×108m . What is the gravitational force of the moon on the earth?The moon's force is what percent of the sun's force?

Answer 1

1. The gravitational force of the sun on the earth is
`3.52*10^(22)\ N`

2. The gravitational force of the moon on the earth is
`1.99*10^(20)\ N`

3. The percentage of moon's force is 0.57%

How to calculate the gravitational force and percent?

1. The gravitational force of the sun on the earth can be calculated as follow:

• Mass of sun (M₁) = 1.99×10³⁰ Kg
• Mass of earth (M₂) = 5.97×10²⁴ Kg
• Distance apart (r) = 1.50×10¹¹ m
• Gravitational constant (G) = 6.67×10¯¹¹ Nm²/Kg²
• Gravitational force (F) =?

`F = G(M_1M_2)/(r^2) \\\\F = 6.67*10^(-11)\ *\ (1.99*10^(30)\ *\ 5.97*10^(24))/((1.5*10^(11))^2)\\\\F = 3.52*10^(22)\ N`

2. The gravitational force of the moon on the earth can be calculated as follow:

• Mass of moon (M₁) = 7.36×10²² Kg
• Mass of earth (M₂) = 5.97×10²⁴ Kg
• Distance apart (r) = 3.84×10⁸ m
• Gravitational constant (G) = 6.67×10¯¹¹ Nm²/Kg²
• Gravitational force (F) =?

`F = G(M_1M_2)/(r^2) \\\\F = 6.67*10^(-11)\ *\ (7.36*10^(22)\ *\ 5.97*10^(24))/((3.84*10^(8))^2)\\\\F = 1.99*10^(20)\ N`

3. The percentage of moon's force as regarding the sun's force can be calculated as follow:

• Gravitational force of sun on earth (
  `F_s`) =
  `3.52*10^(22)\ N`
• Gravitational force of sun on earth (
  `F_m`) =
  `1.99*10^(20)\ N`
• Percentage of moon's force =?

`Percentage\ of\ moon's\ force = ((F_m)/(F_s))\ *\ 100 \\\\= ((1.99*10^(20))/(3.52*10^(22)))\ *\ 100 \\\\= 0.57\%`