Respuesta :
The gravitational force of attraction on Earth due to the Sun and the Moon is [tex]\boxed{3.544 \times {{10}^{22}}\,{\text{N}}}[/tex].
Further Explanation:
The gravitational force of attraction experienced by one body due to the other body is given by the Newton’s law of Gravitation. The newton’s law of Gravitation states that the force experienced by the bodies is directly proportional to the product of the masses of the two bodies and inversely proportional to the square of distance between the bodies.
The force experienced by the Earth due to the moon is;
[tex]{F_{EM}} = \dfrac{{G{M_E}{M_M}}}{{r_{EM}^2}}[/tex]
Here, [tex]{F_{EM}}[/tex] is the force experienced by Earth due to moon, [tex]{r_{EM}}[/tex] is the distance between Earth and Moon.
The mass of the Earth is [tex]5.987 \times {10^{24}}\,{\text{kg}}[/tex].
The mass of the Moon is [tex]7.35 \times {10^{22}}\,{\text{kg}}[/tex].
The distance between the Earth and Moon is [tex]3.84 \times {10^8}\,{\text{m}}[/tex].
Substitute the values in the above expression.
[tex]\begin{aligned}{F_{EM}}&=\frac{{\left( {6.674 \times {{10}^{ - 11}}} \right)\times\left( {5.987 \times {{10}^{24}}} \right) \times \left( {7.35 \times {{10}^{22}}} \right)}}{{{{\left( {3.84 \times {{10}^8}} \right)}^2}}}\\&= \frac{{2.937 \times {{10}^{37}}}}{{1.47 \times {{10}^{17}}}}\\&= 1.986 \times {10^{20}}\,{\text{N}}\\\end{aligned}[/tex]
The force experienced by the Earth due to the Sun is;
[tex]{F_{ES}} =\dfrac{{G{M_E}{M_S}}}{{r_{ES}^2}}[/tex]
Here, [tex]{F_{ES}}[/tex] is the force experienced by Earth due to Sun, is the distance between Earth and Sun.
The mass of the Sun is [tex]1.99 \times {10^{30}}\,{\text{kg}}[/tex].
The distance between the Earth and Sun is [tex]1.5 \times {10^{11}}\,{\text{m}}[/tex].
Substitute the values in the above expression.
[tex]\begin{aligned}{F_{EM}}&= \frac{{\left( {6.674 \times {{10}^{ - 11}}} \right) \times \left( {5.987 \times {{10}^{24}}} \right) \times \left( {1.99 \times {{10}^{30}}\,{\text{kg}}} \right)}}{{{{\left( {1.5 \times {{10}^{11}}{\text{m}}}\right)}^2}}}\\&=\frac{{7.929 \times {{10}^{44}}}}{{2.25 \times {{10}^{22}}}}\\&= 3.524 \times {10^{22}}\,{\text{N}}\\\end{aligned}[/tex]
The net force acting on the Earth is given as:
[tex]{F_{{\text{net}}}} = {F_{EM}} + {F_{ES}}[/tex]
Substitute the values of forces.
[tex]\begin{aligned}{F_{{\text{net}}}}&= 1.986 \times {10^{20}}\,{\text{N}} + 3.524\times {10^{22}}\,{\text{N}}\\&= 3.544 \times {10^{22}}\,{\text{N}} \\\end{aligned}[/tex]
Thus, the gravitational force of attraction on Earth due to the Sun and the Moon is [tex]\boxed{3.544 \times {{10}^{22}}\,{\text{N}}}[/tex].
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Answer Details:
Grade: Senior School
Subject: Physics
Chapter: Newton’s Law of Gravitation
Keywords: Gravitation, sun-moon-earth, gravitational force, new moon, directly between the earth and Sun, newton’s law, 3.544x10^22, net force.
The gravitational force of attraction on Earth due to the Sun and the Moon is 3.544*10^22 N .
What is Newtons law of gravitation?
The gravitational force of attraction experienced by one body due to the other body is given by the Newton’s law of Gravitation. The newton’s law of Gravitation states that the force experienced by the bodies is directly proportional to the product of the masses of the two bodies and inversely proportional to the square of distance between the bodies.
The force experienced by the Earth due to the moon is;
[tex]F_E=\dfrac{GM_EM_M}{r_{EM}^2}[/tex]
Here, [tex]F_{ES}[/tex] is the force experienced by Earth due to moon, is the distance between Earth and Moon.
The mass of the Earth is .[tex]5.987\times 10^{24} kg[/tex]
The mass of the Moon is .[tex]7.35\times 10^{22} \ kg[/tex]
The distance between the Earth and Moon is [tex]3.84\times 10^8\ m[/tex]
Substitute the values in the above expression.
[tex]F_{EM}=\dfrac{(6.674\times 10^{-11})\times (5.987\times 10^{24})\times (7.35\times 10^{22} )}{(3.84\times 10^8)^2}[/tex]
[tex]F_{EM}=1.986\times 10^{20}\ N[/tex]
The force experienced by the Earth due to the Sun is;
[tex]F_{ES}=\dfrac{GM_EM_S}{r_{ES}^2}[/tex]
Here, [tex]F_{ES}[/tex] is the force experienced by Earth due to Sun, is the distance between Earth and Sun.
The mass of the Sun is [tex]1.9\times 10^{30}\ kg[/tex]
The distance between the Earth and Sun is [tex]1.5\times 10^{11}\ m[/tex]
Substitute the values in the above expression.
[tex]F_{ES}=\dfrac{(6.674\times 10^{-11})\times (5.987\times10^{24})\times(1.99\times10^{30}) }{(1.5\times 10^{11})^2}[/tex]
[tex]F_{ES}=3.524\times 10^{22}\ N[/tex]
The net force acting on the Earth is given as:
[tex]F_{net}=F_{EM}+F_{ES}[/tex]
Substitute the values of forces.
[tex]F_{net}=1.986\times 10^{20}+3.524\times 10^{22}[/tex]
F_{net}=3.5444\times 10^{22}\ N
Thus, the gravitational force of attraction on Earth due to the Sun and the Moon is [tex]3.544\times 10^{22}\ N[/tex]
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