a. The gravitational force of the sun on the earth is \(3.54\times 10^{22}\) Newton.
b. The gravitational force of the moon on the earth is \(2.0 \times 10^{20}\) Newton.
c. The percent of the moon's force to that of the sun's force is 0.57%
Given the following data:
- Mass of sun = \(1.99 \times 10^{30}\) kg
- Distance = \(1.55 \times 10^{11}\) meter.
- Mass of moon = \(7.36 \times 10^{22}\) kg
- Distance = \(3.84 \times 10^{8}\) meter.
- Mass of earth = \(6.0\times 10^{24}\) kg
- Gravitational constant = \(6.67\times 10^{11}\)
a. To find the gravitational force of the sun on the earth:
Mathematically, Newton's Law of Universal Gravitation is given by the formula:
\(F = G\frac{M_1M_2}{r^2}\)
Where:
- F is the gravitational force.
- g is the gravitational constant.
- M is the masses of object.
- r is the distance between centers of the masses.
Substituting the given parameters into the formula, we have;
\(F = 6.67\times 10^{-11} \frac{(1.99 \times 10^{30} \times 6.0 \times 10^{24})}{(1.5 \times 10^{11})^2}\\\\F = 6.67\times 10^{-11} \frac{(1.194 \times 10^{55}) }{2.25 \times 10^{22}}\\\\F = \frac{7.96 \times 10^{44} }{2.25 \times 10^{22}}\)
F = \(3.54\times 10^{22}\) Newton.
b. To find the gravitational force of the moon on the earth:
\(F = 6.67\times 10^{-11} \frac{(7.36 \times 10^{22} \times 6.0 \times 10^{24})}{(3.84 \times 10^{8})^2}\\\\F = 6.67\times 10^{-11} \frac{(4.42 \times 10^{47}) }{1.47 \times 10^{17}}\\\\F = \frac{2.95 \times 10^{37} }{1.47 \times 10^{17}}\)
F = \(2.0 \times 10^{20}\) Newton.
c. To find what percent is the moon's force to that of the sun's force:
\(Percent = \frac{2.0 \times 10^{20}}{3.54\times 10^{22}} \times 100\)
Percent = 0.57%
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