[Paolo]

Paolo asked the Naked Scientists:
   
How can I figure out the geodetics around a planet far away from other bodies?

What do you think?

[yor_on]

Do you mean geodesics or geodynamics?

Take a look here if it's geodynamics you meant.

[JMLCarter]

Geodesic is the roughly planet shaped surface of equal gravity which is located on average at the altitude of the planets surface.

Measuring earth's geodisic is not easy, the variations in density in the earth impact it.
It is a task undertaken by the GEOSAT and GFO satellites, which use radar, GPS and other techniques.

[JP]

I don't think it can be a surface of equal gravity, because it's the path that objects under free-fall take.  An object falling in towards the sun experiences "more gravity" (whatever that means in general relativity) as it gets closer to the sun.

[syhprum]

"How can I figure out the geodetics around a planet far away from other bodies?"

I think the MESSENGER spacecraft that has just gone into orbit around Mercury is doing just that

http://www.nasa.gov/mission_pages/messenger/main/index.html

[JMLCarter]

Objects in orbit fall into the central mass but keep missing. The definitions are thus consistent.
I guess the term geodetic that refers to surface gravity maps needs some further constraint as it is not any arbitrary geodetic, but a surface on average closest to the surface. Does any-one know the proper full name?

[imatfaal]

Hi Paolo - you really need to clear up whether you meant geodeSic or geodeTic.  They both exist. 

I think you mean geodesic - which is the path that an object will follow when no forces apart from gravity is acting upon it (as JP said in freefall).  Its either an estimation using Newton or heavy duty maths involving General Relativity.   In Newtonian flat space we can calculate orbits using Keplar's laws.  In GR we need to work out what "a straight line" in curved space looks like - and that's beyond my paygrade.   

[JP]

Objects in orbit fall into the central mass but keep missing. The definitions are thus consistent.

Good point, which makes it clear that geodesics do depend on the initial velocity of the object.  The trajectory of a satellite under free fall is quite different than the trajectory of a ball dropped from a great height because of their initial velocities.

Geodesics are the closest thing to  "straight lines" in space-time, as Matthew said, with a bunch of complex math to work out the details (they're shortest paths, essentially).  But you can visualize them as the path taken through space and time of any object free-falling, be it a satellite or a ball dropped off a cliff.

[PAOLO137]

First of all I wish to thank all the kind friends who have spent some of their time to answer my question.
I have found many useful hints in your answers. To better clarify what I meant let me refer to the usual
figure used to understand the 4 dimension space, that is the flat physical world we can imagine to live in with
easyness, plus the vertical time axis and the classical double cone indicating the possible past and future
location of events.
Now, what I am looking for is something similar for General Relativity. I take the opportunity to say that the use of
free-fall for an object in space may be misleading. How better would be "free-floating"!
Making use of what I know about the method of making a satellite "swing" close to a planet to gain speed and take
the desired course (is the word "swing" correct?) I imagine that the trajectory of such a satellite must be a geodesic, and many other geodesics could be made "visible" launching satellites faster or slower, farther or closer
to that planet. What really puzzles me is : in Newton phisycs a body could move in a straight line if undisturbed, an that was a geodesic of a 3D space, and could also not move al all if I choose the correct inertial coordinates . Why an apple must fall down (of course along a geodesic) if I let it free in the space in my room? Is there a geodesic running there directed as a the radius of the Hearth? Sorry for the amount of stupid things I must have written. Paolo.

[yor_on]

You are wondering how 'space' is warped/distorted right

Well, so am I. You can, from a Newtonian point of view, think of any planet as a bicycle wheel. The center of that wheel will be a place where all the 'gravity' take each other out leaving you with 'zero gravity'. The spokes going out from that center could be seen as the direction gravity takes. and those are the 'geodesics/paths' a object will follow as it moves closer to the planets center, whether from space or as an apple falling. But in reality a planet rotates (frame dragging) and interact gravitationally with other planets so the reality is more complicated. A geodesic is just the easiest path a object can take in SpaceTime, all other paths will cost it energy to try. So it's no big mystery there, except what 'gravity' really is of course. Einstein thought it to be a geometry macroscopically, and that is the best explanation I know of it. In Quantum mechanics physicists hope to find this 'geometry' being created by 'particles' on the very small plane, either as a Higgs field/boson or as some other type of 'gravitons'.

It depends on how you think reality is created, in a 'grainy field' or in a smooth. I expect it to be a smooth field myself, although 'particles' will exist too.

[JP]

to that planet. What really puzzles me is : in Newton phisycs a body could move in a straight line if undisturbed, an that was a geodesic of a 3D space, and could also not move al all if I choose the correct inertial coordinates . Why an apple must fall down (of course along a geodesic) if I let it free in the space in my room? Is there a geodesic running there directed as a the radius of the Hearth? Sorry for the amount of stupid things I must have written. Paolo.

Hi Paolo.  Don't worry, you're not saying stupid things.  These are pretty difficult topics you're bringing up, and take a lot of time to understand. 

First, the difference between Newtonian gravity and general relativity is that Newtonian gravity is designed to model relatively weak gravity, while general relativity is designed to model strong gravity.  Newtonian gravity uses Newton's laws, which says that things either sit still or move in a straight line until a force acts on them.  It treats gravity as a force that can deviate things from straight lines. 

Geodesics are a geometrical-physics idea that says that if something is moving without forces, it moves in a straight line, or in the closest thing to a straight line that it can.  So even in Newtonian gravity, geodesics exist: they're the straight lines things would move along without forces acting on them.

General relativity says that instead of treating gravity as a force that makes things deviate from straight lines, we can treat it as space-time itself being bent.  If you bend space-time, then what used to be straight lines are actually curved.  They're still the closest thing you can get to a straight line in curved space-time, however.  So general relativity tells you that gravity isn't a force, but that it does curve space-time.  Things still move along geodesics if there are no outside forces acting on them.

The difference in releasing an apple is that Newtonian gravity says that a force is pulling the apple towards the earth.  Without gravity, it would just remain floating where you released it, but with gravity it gets pulled towards the earth.

General relativity says that there is no force, but that the apple, rather than sitting still when you release it, follows it's geodesic in curved space-time, which happens to carry it towards the earth.