Comments from feedback form - "So it may be shrinking. Its ma..."

It's a well established fact that gravity increases with density. In other words, if the earth was smaller in diameter, given the same mass (i.e., higher density) its gravitational field would be higher (assuming the field is measured at a fixed distance from its center). If you take this to the extreme, by compressing the earth to 1 mm in diameter, it's gravitational field would be phenomenally high. The earth's mass may even be a black hole at that size.

Mass always has density, even if it's just a bunch of hydrogen atoms loosely dispersed in space. When those hydrogen atoms condense into a star, that mass is now at a much higher density and consequently produces a much stronger gravitational field. If the star eventually collapses into a black hole, you wouldn't want to be anywhere in that vicinity of space. Time to dust off the physics and astronomy textbooks. The strength of a gravitation field is directly proportional to the increase in density of a given mass as measured from a fixed point to the center of that mass (and, outside that mass - not measured from somewhere inside the mass).

99.254.218.71 (talk)21:25, 23 August 2010

Please recommend a textbook reference for the proposition that field strength of a fixed mass at a fixed distance from the center increases with density.

As a counterexample, I have a copy of Stephen Eales' Planets and Planetary Systems to hand. Eales quotes the high school equation for Newton's law of universal gravitation without qualification, which I read as force per unit mass (outside the object) is proportional to mass divided by the square of the distance from the centre of mass. (ISBN 9780470016930, Wiley-Blackwell 2009, p.106)

InfantGorilla (talk)07:30, 24 August 2010

InfantGorilla, thank you for your reference. I will seek out a counter reference and get back to you asap. We must keep in mind that Newtonian equations break down when it comes to explaining extreme phenomena, such as black holes. Within an Einsteinian curved, spacetime framework, gravity is no longer a force and can act instantaneously at a distance. This discovery has had severe consequences for modern cosmology. I'll get back to you, even if it is to prove myself wrong.

99.254.218.71 (talk)16:49, 25 August 2010

Thanks. I don't know Einstein's equations for gravity. An effect of increased density, even if too small to measure for normal matter, will be interesting.

Meanwhile, I suspect the complexities of classical dynamics dominate relativity in the Earth-Moon system: I have read that the slow retreat of the Moon is caused by tidal forces.

InfantGorilla (talk)17:25, 25 August 2010
 
 

You're thinking of this backwards.

Earth's equatorial radius is currently 6,378 kilometres. If you crushed the Earth to the size of a pea, it would be a black hole. But someone orbiting from a distance of 6678 kilometres from the centre of mass (300 kilometres above the current surface, or Near Earth Orbit) would experience the same force of gravity in either circumstance. Regardless of whether you are 6678 kilometres from the centre of the Earth or 6678 kilometres from the centre of an Earth massed black hole, the gravity you experience will be identical. At a given distance from an object the force of gravity will be the same, regardless of the density of the object, provided that all the mass of the object is below you.

The reason that a black hole "has a stronger gravitational field" (even though it doesn't really) is because you can get much closer to the centre of mass without crashing into the surface. That's it.

Gopher65talk01:31, 27 August 2010