Gravitational Forces: Why Doesn't Sun Revolve Around Earth?

[okgo]

Homework Statement

So finals is coming up and I was reviewing my notes, when I read that according to Netwon's Third Law gravitational forces (Fg) should be equal between to objects like the sun and the Earth. So if the sun and Earth have the same Fg toward each other, why doesn't the sun revolve around the Earth instead?

I looked at the Cavendish balance and it says the small object moves toward the bigger object even though they have the same Fg toward each other.

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

Yes, for two bodies of masses m and M, the distance between their centers r, the gravitational force between them is
[tex] \frac{GmM}{r^2}[/math]

However, since force= mass times acceleration, acceleration= force/mass.

That is, the acceleration of the object of mass M is
\(\displaystyle \frac{GmM}{Mr^2}= \frac{Gm}{r^2}\)
while the acceleration of the object of mass m is
\(\displaystyle \frac{GmM}{mr^2}= \frac{GM}{r^2}\)

That is, if M is much larger than m (as for sun and earth) the lighter body will have a much greater acceleration.

Actually both bodies rotate around their mutual center of gravity. In the case of Earth and sun, that center of gravity is well within the sun.

 

[nlightner]

First of all, it is important to understand that gravitational forces are not the only factor that determines the motion of objects in space. There are other factors such as velocity, mass, and distance that also play a role.

In the case of the sun and Earth, while they do have equal gravitational forces towards each other, the sun has a much larger mass and therefore exerts a stronger gravitational force on the Earth. This stronger force causes the Earth to revolve around the sun, rather than the other way around.

Additionally, the Earth also has a significant velocity, which creates a centrifugal force that counteracts the gravitational force from the sun. This balance between gravitational and centrifugal forces allows the Earth to maintain its orbit around the sun.

Furthermore, it is important to note that the Cavendish balance experiment is conducted on Earth, where the gravitational force between the two objects is much smaller compared to the gravitational force between the sun and Earth. This is why the small object moves towards the larger one in the experiment, as the gravitational force is the dominant force.

In conclusion, while Newton's Third Law states that gravitational forces are equal between two objects, there are other factors at play that determine the motion of objects in space. The sun's larger mass, the Earth's velocity, and the balance between gravitational and centrifugal forces all contribute to the Earth's orbit around the sun.