How Does the Moon's Motion Affect Earth's Equatorial Plane?

[medwatt]

Hello,
Suppose we pass a horizontal plane through the Earth's equator. Over a period of a year how is the variation of the Earth up and down the plane affected by the moon's motion and other planet's at closest approach to Earth and is it really possible if the moon had the same mass of the Earth for them to coexist as they are now.

 

[Simon Bridge]

Hello,
Suppose we pass a horizontal plane through the Earth's equator. Over a period of a year how is the variation of the Earth up and down the plane affected by the moon's motion and other planet's at closest approach to Earth and is it really possible if the moon had the same mass of the Earth for them to coexist as they are now.

It is difficult to know how to answer the first one - are you talking about tidal variations? If so - in the crust or the water? Or maybe you mean the displacement of the com of the Earth from the orbit trajectory due to it's co-rotation with the Moon?

I suspect you mean orbital perturbations - which you should be able to look up ;) i.e. the wiggle introduced by the co-rotation with the moon would be twice the displacement of the E-M com from the E com. But, in this case, wouldn't you want to pick the plane of the ecliptic rather than a plane through the equator ...

For the second: what do you mean by "as they are now"?
Right now the center of mass of the Earth-Moon system is close enough to the center of mass of the Earth alone so that saying "the Moon orbits the Earth" makes sense. That would not be the case if the Moon had equal mass to the Earth. There would also be a much more dramatic impact on the tides. But maybe you are thinking of something else.

 

[medwatt]

1. Let me explain my first question with an analogy. If we put a charge in an electric field, the field will produce a force on the charge and conversely the charge will produce an equal and opposite force on the charges producing the field so that they are pushed/pulled in some direction. Now an object is falling towards the Earth the Earth does work on the object and because of that the gravitational potential of the object reduces. Whereas for the Earth its potential increases. My question is how does this increase in potential affects the Earth's motion if we are viewing the Earth from the sun, for example, using the sun as a fixed reference frame. (I hope that sounds ok)

2. I wanted to know it its possible for to two planets the size/mass of the Earth to be within the same distance as the Earth and the moon and continue without collision like a binary star system.

 

[Simon Bridge]

1. Let me explain my first question with an analogy. If we put a charge in an electric field, the field will produce a force on the charge and conversely the charge will produce an equal and opposite force on the charges producing the field so that they are pushed/pulled in some direction. Now an object is falling towards the Earth the Earth does work on the object and because of that the gravitational potential of the object reduces. Whereas for the Earth its potential increases. My question is how does this increase in potential affects the Earth's motion if we are viewing the Earth from the sun, for example, using the sun as a fixed reference frame. (I hope that sounds ok)

How do you figure the Earth PE increases when an object falls towards it?
Usually the Earth and the object fall towards each other under their mutual gravitational attraction - each loses gravitational PE in exchange for kinetic energy.

But it does seem you wanted to know about the orbital "wobble" as the Earth orbits the common center of mass of the Moon ... the answer is already given to you. You can look up planetary perturbations to get an order-of-magnitude estimate for their size as well. But if you want to see the combined effect, what you do it put a plane perpendicular to the Earth's orbit, to one side, and put a point on the plane where the center of mass of the Earth passes through the plane ... it's called a Poincare Map and you can find pics of them for different planets online.

In a purely classical system of just the Earth and the Sun, the Poincare Map is just a single dot as the Earth passes through the plane at the same spot every orbit. However, since the actual solar system is a many-body system, the actual orbit is much more complex than that. Enjoy.

2. I wanted to know it its possible for to two planets the size/mass of the Earth to be within the same distance as the Earth and the moon and continue without collision like a binary star system.

Size and mass eh? I'd have to check since there are limits on placement of objects for stable orbits that I don't have at my fingertips. My gut reaction is that it should work - though it would probably be unpleasant. I suspect that tidal forces should force the two planets apart over time.

 

[medwatt]

Thanks. BTW where can I read such stuffs that are outside typical physics books ?

 

[Simon Bridge]

This is all fairly standard text-book stuff ... for senior undergrad and grad level college.
The Poincare stuff is in "Chaos Theory" for example, and you can google for images - the sites the images come from will tell you about them.

"Orbital Mechanics" often has it's own papers ... I think that is the broad subject you are showing an interest in.
Look for college course-notes and lectures online.