How Does Mass Affect the Fabric of Space-Time?

[Paramedic_Nerd]

I'll ask that you forgive me if my question seems to "basic" or simple for some of the more professional posters. I am simply a physics/cosmology enthusiast who has been captured by it all since I was a child, however, there is one issue that as I continue to learn more is bothering me.
I am of course familiar with the illustration that depicts a body of mass depressing a region of space time as described by the "grid" and I understand this to be the easiest way to depict this phenomena. My questions are as follow:

1) Does a body of mass not "pull" or "depress" space time in ALL directions, indicating that the visual representation or illustration most commonly use is merely one perspective on one plane of one dimension at the time of observation?

2) This question may be nullified by the answer to the first, but presuming space time is affected by mass the way the common illustration describes, I often ask; What about the other side of that curvature? If the "depression" of space time holds bodies in place ( moons and other satellites), then would the "peak" or convex portion of space time not repel bodies?

3) Also dependent on the answer to question number one, if space time is in fact bent or warped in ALL directions; Why do the planets of our solar system orbit on a seemingly level plane? Why should it be there are no planet or bodies that obit perpendicular, or any other angle really, to Earths' orbit.

I thank you for your time and patients as you read and consider responding. I hope to find or create a network of peers, who despite my apparent or preserved ineptness on some subjects, enjoy sharing their knowledge and experiences. Through years of recreational researcher and haphazard investigations of my own, I continue to build on a solid foundation of basic understanding. With the capacity to learn, the ability to accept and understand as well as the innate desire to know, the need to know, I look forward to exploring through both imagination and intellect the farthest reaches of physics, the cosmos and all that is in between and beyond.

 

[Nugatory]

I am of course familiar with the illustration that depicts a body of mass depressing a region of space time as described by the "grid" and I understand this to be the [STRIKE]easiest[/STRIKE] most misleading way to depict this phenomena.

Fixed it for you ..
Seriously, kidding aside, that picture is seriously misleading. If you search this forum for "rubber sheet analogy" you'll find some posts explaining why, and you may also come across member A.T.'s somewhat excellent video showing what's really going on.

1) Does a body of mass not "pull" or "depress" space time in ALL directions, indicating that the visual representation or illustration most commonly use is merely one perspective on one plane of one dimension at the time of observation?

It's not a "pull" or a "depression", it's curvature. One way of imagining it: If you and I start one mile apart on the equator and both walk due north in a straight line, we'll become conscious of a force that is inexorably shoving us towards one another until we collide at the north pole. What's really going on, of course, is that on the curved surface of the Earth parallel lines do intersect, although they don't on a flat surface. (This analogy is misleading for other reasons, but it's still a lot better than the rubber sheet). Note that it is space-time that is curved, not just space - the "paths" of two objects that are ostensibly at rest and subject to no forces can still converge or diverge because they're still moving forward in time.

2) This question may be nullified by the answer to the first, but presuming space time is affected by mass the way the common illustration describes, I often ask; What about the other side of that curvature? If the "depression" of space time holds bodies in place ( moons and other satellites), then would the "peak" or convex portion of space time not repel bodies?

The "depression" isn't what holds the body in place, and that may be the most misleading aspect of the rubber-sheet analogy. There's no depression, no "other side".

3) Also dependent on the answer to question number one, if space time is in fact bent or warped in ALL directions; Why do the planets of our solar system orbit on a seemingly level plane? Why should it be there are no planet or bodies that obit perpendicular, or any other angle really, to Earths' orbit.

There are many such objects in such orbits - they just happen not to be as big as the planets. The planets all ended up in more or less the same plane (but the deviations for some of them are still quite large) just because of the initial conditions under which the solar system formed.

 

[Paramedic_Nerd]

Thanks very much. You have provided some excellent clarification as well as some thought provoking jump off points for me to further investigate. I look forward to hearing from you again regarding future questions and concerns.

 

[A.T.]

1) Does a body of mass not "pull" or "depress" space time in ALL directions, indicating that the visual representation or illustration most commonly use is merely one perspective on one plane of one dimension at the time of observation?

Yes, it is just 2D spatial geometry at constant time, which is a subset of 4D space-time. The distortion of the time dimension is not shown there. 2D space-time looks more like this:

https://www.youtube.com/watch?v=DdC0QN6f3G4

And on a larger scale:
http://www.adamtoons.de/physics/gravitation.swf

What about the other side of that curvature? If the "depression" of space time holds bodies in place ( moons and other satellites), then would the "peak" or convex portion of space time not repel bodies?

There is no "other side", it is a one sided surface. Only the geometry within the surface matters. So it doesn't matter if you draw it deformed down or up.

See also:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

3) Also dependent on the answer to question number one, if space time is in fact bent or warped in ALL directions; Why do the planets of our solar system orbit on a seemingly level plane? Why should it be there are no planet or bodies that obit perpendicular, or any other angle really, to Earths' orbit.

The space-time geometry is spherically symmetrical. You have the same 2D space with a dent for every plane that goes through the center. And you get the same 2D space-time along every radial line through the center. As Nugatory said, the alignment of orbit planes has to do with initial conditions and the way a solar system forms.