The strength of the force between person and the moon is equal to 106.6 Newton.
Given the following data:
- Mass of moon = [tex]7.34 \times10^{22}\; kg[/tex]
- Radius = [tex]1.74\times 10^6\; meters[/tex]
Scientific data:
- Gravitational constant = [tex]6.67\times 10^{-11}[/tex]
To determine the strength of the force between person and the moon, we would apply Newton's Law of Universal Gravitation:
Newton's Law of Universal Gravitation states that the force of attraction (gravitational force) acting between planet Earth and all physical objects is directly proportional to the mass of planet Earth, directly proportional to the mass of the physical object and inversely proportional to the square of the distance separating the Earth's center and that of the physical object.
Mathematically, Newton's Law of Universal Gravitation is given by the formula:
[tex]F = G\frac{M_1M_2}{r^2}[/tex]
Where:
- F is the gravitational force.
- G is the gravitational constant.
- M is the mass of objects.
- r is the distance between centers of the masses.
Substituting the given parameters into the formula, we have;
[tex]F = 6.67\times 10^{-11} \frac{(7.34 \times 10^{22} \times 66)}{(1.74 \times 10^{6})^2}\\\\F = 6.67\times 10^{-11} \frac{(4.84 \times 10^{24}) }{3.03 \times 10^{12}}\\\\F = \frac{3.23 \times 10^{14} }{3.03 \times 10^{12}}[/tex]
Force, F = 106.6 Newton.
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