Gravitational force of the sun on earth

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SUMMARY

The gravitational force of the Sun on the Earth, as well as the gravitational force of the Earth on the Sun, can be calculated using Newton's law of universal gravitation. Given the masses of the Sun (1.99e30 kg) and Earth (5.97e25 kg), and the distance between them (1.50e11 m), the formula Fg = (Gm1m2) / (r^2) applies, where G is the gravitational constant (6.67e-11 Nm^2/kg^2). The forces are equal in magnitude but opposite in direction, adhering to Newton's 3rd Law of Motion. The presence of the Moon does not affect the mutual gravitational force between the Sun and Earth, although it does contribute to the net gravitational forces acting on the Earth.

PREREQUISITES
  • Understanding of Newton's law of universal gravitation
  • Familiarity with gravitational constant (G = 6.67e-11 Nm^2/kg^2)
  • Knowledge of mass and distance measurements in physics
  • Basic comprehension of vector forces and Newton's 3rd Law of Motion
NEXT STEPS
  • Calculate the gravitational force between the Earth and the Moon using the same formula
  • Explore the implications of gravitational forces in multi-body systems
  • Study the effects of gravitational interactions on orbital mechanics
  • Investigate how gravitational forces influence tides on Earth
USEFUL FOR

Students studying physics, educators teaching gravitational concepts, and anyone interested in celestial mechanics and the interactions between astronomical bodies.

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Homework Statement


Consider the system of the Sun, Earth, and Moon, at a moment in time when they happen to be exactly in a line. (Assume that all distances d are measured between the centers of all bodies, and that all distances d are much greater than the radii of all bodies.
M(sun) = 1.99e30 kg
M(earth) = 5.97e25 kg
M(moon) = 7.35e22 kg
d(earth-sun) = 1.50e11 m
d(earth-moon) = 3.84e8 m
G = 6.67e-11 Nm^2/kg^2

Calculate the magnitude of the gravitational force of the Sun on the Earth. Also, what is the gravitational force of the Earth on the Sun?

Homework Equations


Fg = (Gm1m2) / (r^2)


The Attempt at a Solution


I know that all I have to do is plug in the value into the Fg equation above. However, I'm a little lost with the force of the Sun on the Earth, and the force of the Earth on the sun. Does the value of r change for both of these cases or stay the same?
 
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If you forget Moon for a moment, then the force of Sun on Earth should be the same as the force of Earth on Sun.
If you do not forget Moon, those forces are still the same, but there is the force of the Moon as well, so the sum force acting on Earth is F(Sun-Earth) + F(Moon-Earth). In a vector sense, so you should substract the force by Moon if it is in the other side. I suspect from the wording that it is on the other side, but it is not exactly clear.
 
The force of the Sun on the Earth is the same as the force of the Earth on the Sun. It must be, according to Newton's 3rd Law of Motion.
 

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