Not that this matters a whole lot to a lot of people, but a real, physically accurate gravitational field can and does
indeed "catch" stray objects and make them spiral into itself, but the effect is quite negligible for the Earth in orbit around the Sun. Basically, any large accelerating mass and/or large rotating axially asymmetric mass (ie. anything producing a time-dependent metric) will shed energy-momentum-mass-pressure-viscosity as gravitational radiation, and the result will be shrinking bodies and shrinking orbits. Black hole mergers are the most extreme example of this, and the effect has been observed in the behaviour of binary stars. http://en.wikipedia....ional_radiation
This is all somewhat, but not entirely similar to how an electron can shed momentum in the form of light when it is accelerated. This is why physicists figured that the energy-momentum levels of the electron in an atom had to be quantized. Otherwise, if an electron in an atom could shed all of its momentum, then it would definitely spiral into the nucleus and come to a screeching halt, which simply doesn't happen. http://en.wikipedia....i/Bremstrahlung
FYI: If you can integrate the following two paragraphs into a single coherent paragraph -- without obvious inconsistencies like "doesn't the electron shed momentum and/or rest mass as gravitational radiation?" -- then you'll win a Nobel prize and eternal fame.http://en.wikipedia....Quantum_gravity
And yeah, these guys are absolutely right that constant acceleration is not appropriate for replicating Angry Birds Space. Constant acceleration (SUVAT equations, or even an acceleration vector of variable direction but constant length, for that matter) is only appropriate for Angry Birds/Rio/Seasons where a) the curvature of the sphere's surface is low and the local section in question (ie. the playing field) is so small that the sphere's surface (ie. floor) is practically flat, and b) the local section in question does not extend above the surface/floor to any significant extent. Basically, the playing field's total width and total height would both have to be very small compared to the sphere's radius for constant acceleration to be appropriate. See: http://en.wikipedia....Gravityroom.svg
If these two criteria aren't met, then you have to consider that a) the lines of force perpendicular to the surface actually converge (they aren't really parallel, because even space is curved in Newtonian gravity) and that b) the inverse square law means that large changes in distance can lead to large changes in acceleration (we'll skip going into the curvature of time because it isn't really related to Newtonian gravity per se, but it might be something that you'll want to look into later). In this case, you should use non-constant acceleration similar to target_acceleration_vector = G*source_mass / length(source_pos - target_pos)^2 * normalize(source_pos - target_pos) * dt, where dt is the length of your physics engine's time step.** See: http://en.wikipedia....macroscopic.svg
Obviously, Angry Birds Space contains one or more non-flat/highly curved floors per playing field, given that a lot of it is made up of circular "planets" with radii much smaller than the width and height of the playing field, and so constant acceleration is definitely not appropriate.
** LaTeX test, for fun (can't seem to do rmtext):
Direction vector pointing from target position to gravitational source position:
Distance from target to gravitational source:
Unit direction vector pointing from target to gravitational source:
Mass of gravitational source:
Acceleration vector pointing from target to gravitational source. And no, it is not proper to fudge the following equation to look like it's an inverse-cube law when teaching about gravitation, you general haters of normalization operations, heh:
Edited by taby, 09 May 2012 - 06:05 PM.