High School Help in explaining a question on gravity

[trees and plants]

Hello. I have this question: do you know why a physical body with bigger mass makes another one orbit around it like the sun does in the solar system and not the opposite of this? Thank you.

 

[lomidrevo]

The bodies actually orbit around the common center of mass.

 

[trees and plants]

You mean the sun also orbits around the center of the solar system which is different than the sun?

 

[trees and plants]

How is this explained mathematically? Do you know?

 

[Ibix]

Google "barycenter". A planet orbiting a stationary Sun violates conservation of momentum because the Sun has zero momentum and the planet's momentum is changing. Both need to orbit a common center.

In the case of objects with large mass differences, the barycenter is very close to the center of the larger mass. So "Earth orbits the Sun" is close enough to the truth for most purposes.

 

[trees and plants]

So saying heliocentric system is not correct, center of the solar system is correct which is not the sun. I understand now that they were approximations so far, scientists were trying to describe it and so far this is the latest correct view of the orbits of the solar system?

 

[lomidrevo]

You mean the sun also orbits around the center of the solar system which is different than the sun?

Yes, the Solar system's barycenter is not located in Sun's center.
https://spaceplace.nasa.gov/barycenter/en/

How is this explained mathematically? Do you know?

I think only two-body problem can be solved analytically. System with multiple bodies need to be solved numerically.
https://en.m.wikipedia.org/wiki/Two-body_problem

 

[sophiecentaur]

The masses of the Earth and Moon are nearer equal to each other and the phenomenon is more appreciable. The Earth has a definite 'wobble' as it 'orbits' the barycentre, once a month and there are no other large bodies in Earth orbit to spoil the effect. The barycentre is about 3/4 of the distance from the centre of the Earth to its surface - pretty significant, eh?
I don't think that amount of wobble is great enough for it to cause enough parallax to affect observations of other objects in the Solar System, though.