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The Earth has a mass of 6.0 x 1024 kg, and the Moon has a mass of 7.3 x 1023
kg. They are separated by a distance of about 3.84 x 105 kilometers. How
much gravitational force do the two bodies exert on one another?
0 1.0 x 1021 N
O 2.0 x 1021 N
o 3.0 x 1021 N.
O 4.0 x 1021 N

Respuesta :

Lanuel

The amount of gravitational force the two bodies exert on one another is [tex]2.0 \times 10^{27} \;Newton[/tex].

Given the following data:

  • Mass of Moon = [tex]7.3 \times 10^{23}\; kg[/tex]
  • Mass of Earth = [tex]6.0 \times 10^{24}\; kg[/tex]
  • Radius = [tex]3.84 \times 10^5\; kilometers[/tex]

Scientific data:

  • Gravitational constant = [tex]6.67\times 10^{-11}[/tex]

To determine the amount of gravitational force the two bodies exert on one another, we would apply Newton's Law of Universal Gravitation:

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 object.
  • 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} \times \frac{7.3 \times 10^{23} \; \times \;6.0 \times 10^{24}}{(3.84 \times 10^5)^2}\\\\F = 6.67\times 10^{-11} \times \frac{4.38 \times 10^{48} }{1.48 \times 10^{11} }\\\\F=\frac{2.92 \times 10^{38} }{1.48 \times 10^{11}} \\\\F= 2.0 \times 10^{27} \;Newton[/tex]

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