R
rpmath
Guest
Except for distances too close to the Schwarzschild radius, the Newton inverse square law is supposed to be very accurate for Gravity...<br />but what happens if the universe is curve?<br />I think gravity must be a little stronger than supposed for a flat universe.<br /><br />If the Universe is the 3D surface of a 4D hypersphere, y can represent it as the attached picture.<br />Lets say the Universe radius is R, I have a mass at point A and I want to test the gravity field at some point B whose distance to A is d.<br /><br />By Newton:<br />a = -GM / r<sup>2</sup><br /><br />but if the universe is round, the real radius of the sphere centered in A where the gravity is distributed when it reaches B is not the same distance d between A and B, but a smaller value r, that I can calculate as:<br /> r = R sin(d / R)<br />and: <br /> a = -GM / (R sin(d / R))<sup>2</sup><br /><br />if d is much smaller than the universe:<br /> a = -GM / d<sup>2</sup> -GM /(3 R<sup>2</sup>) -GM d<sup>2</sup> /(15 R<sup>4</sup>) - ...<br /><br /> a = -GM / d<sup>2</sup> * ( 1 + 1/3 (d/R)<sup>2</sup> + 1/15 (d/R)<sup>4</sup> + ... )<br /><br />Is seems as a good way to get the size of the universe... but may be “d / R” is too small to measure the “1/3 (d/R)<sup>2</sup>” factor...<br /><br />If average Universe expansion speed is near light speed, R will be near 14 * 10<sup>9</sup> light years the earth orbit radius is near 8 light minutes, so d/R will be near 8 min / ( 14 * 10<sup>9</sup> * 365.25 * 24 * 60 min) = 10<sup>-15</sup><br /><br />can a error in the acceleration of 10<sup>-30</sup> be measured?<br />