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Part A. 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? Express your answer to three significant figures and include the appropriate units. Fsone = . Part B. 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?.Express your answer to three significant figures and include the appropriate units. Fmone = . The moon's force is what percent of the sun's force?

Respuesta :

PART A: 

As we know that gravitational force is given by

[tex]F=\frac{GMm}{r^2}[/tex]

Here we know that

G = Gravitational constant.

M = mass of the sun = [tex]1.99 \times 10^{30} kg[/tex]

m= mass of the Earth = [tex]6 \times 10^{24} kg[/tex]

r = distance between them =[tex]1.5 \times 10^{11}[/tex]

Sonow we have

[tex]F=\frac{(6.67\times 10^{−11})(1.99\times 10^{30})(6\times 10^{24})}{ (1.5\times 10^{11})²}[/tex]

[tex]F=3.53 \times 10^{22}N[/tex]

Part B)

As we know that gravitational force is given by

[tex]F=\frac{GMm}{r^2}[/tex]

Here we know that

G = Gravitational constant.

M = mass of the moon = [tex]7.36 \times 10^{22} kg[/tex]

m= mass of the Earth = [tex]6 \times 10^{24} kg[/tex]

r = distance between them =[tex]3.84 \times 10^{8}[/tex]

Sonow we have

[tex]F=\frac{(6.67\times 10^{−11})(7.36\times 10^{22})(6\times 10^{24})}{ (3.84\times 10^{8})²}[/tex]

[tex]F=1.99 \times 10^{20}N[/tex]

Lanuel

a. The gravitational force of the sun on the earth is  [tex]3.54\times 10^{22}[/tex] Newton.

b. The gravitational force of the moon on the earth is [tex]2.0 \times 10^{20}[/tex] 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 = [tex]1.99 \times 10^{30}[/tex] kg
  • Distance =  [tex]1.55 \times 10^{11}[/tex] meter.
  • Mass of moon = [tex]7.36 \times 10^{22}[/tex] kg
  • Distance =  [tex]3.84 \times 10^{8}[/tex] meter.
  • Mass of earth = [tex]6.0\times 10^{24}[/tex] kg
  • Gravitational constant = [tex]6.67\times 10^{11}[/tex]

a. To find the gravitational force of the sun on the earth:

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 masses 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} \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}}[/tex]

F = [tex]3.54\times 10^{22}[/tex] Newton.

b. To find the gravitational force of the moon on the earth:

[tex]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}}[/tex]

F = [tex]2.0 \times 10^{20}[/tex] Newton.

c. To find what percent is the moon's force to that of the sun's force:

[tex]Percent = \frac{2.0 \times 10^{20}}{3.54\times 10^{22}} \times 100[/tex]

Percent = 0.57%

Read more: https://brainly.com/question/21511416

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