if an object was to fall towards the sun, what would be it's acceleration?

and one random question

compared to everyday objects, how are black holes compared? Are they bigger or smaller than a dime? An elephant? An atom? 50 suns?

__________________
May the schwartz be with you!

That depends entirely on its mass. The formula is R=Gm/(c^2), with R being the radius, G the gravitational constant, m the mass of the star and c the speed of light.

Nitpicikiing: that would be the radius of the Event Horizon; not necessarily the size of the stuff that makes up the black hole. According to General Relativity, a black hole would be infinitismal, while Quantum Mechanics and String theories would have it of a very small, but finite, size. I don't think we have any theory that really works inside the event horizon, so it is hard to say.

Gosh, just found how ignorant I am (form a queue those who knew already).

"Gravitational constant"?? g, small g, is the 'pull' of gravity on the surface of the earth? So how does that relate to, or is calculated from G?

Is there a digested 'Principia', as surely this was part bof that?
(Three hundred years of reading to catch up!)
John

True. But that's the size you'd see if you looked at it from the outside (always a good idea).

G = 6.67259*10^-11 Nm^2/kg^2

g = GM/R^2

Well the force of gravity is directly proportional to the masses it acts between and inversly proportional to the square of their distance. So you get F~m₁*m₂/d². So you know if you double the distance the force will be one quarter of what it was. If you double one mass the force will double too, etc. All the gravitational constant does is that it tells you how strong the force will be between two 1 kg masses placed 1 m from each other. So you get F=G*m₁*m₂/d² since force equals mass (m₂) times acceleration (let's call it g for now) m₂*g=G*m₁*m₂/d² so g=G*m₁/d², where m₁ is the mass of the Earth and d is the distance from the centre of the Earth.

The value of G is about 6.67*10^-11 Nm²/kg². It's an extremely small value, which is why you don't feel gravitational attraction to everyday objects around you. Its dimension may seem strange until you look at the formula for the gravitional force. Everything except N cancels out so it gives the force in Newton units.

Write "m(sub)1(/sub) and d(sup)2(/sup)" and replace parenthesis with square brackets: m₁ and d²

Thanks.