[SOLVED] Two objects of Different masses falling We all know that due to Newtons laws that the mass of an object has nothing to do with how fast the object falls. Two objects fall at the same rate. Is there a chance that they really don't fall at the same rate and that this is such a small change that we cannot detect it with modern experiments?
As far as I know, aslong as you have identical conditions for both experiments it shouldn't affect the speed at witch they fall. Modern equipment can easily detect any anomalies. Tachyon.
If we are to be anal, they don't fall at the same rate at all. I'm excluding the trivial case of air resistance and focus on the free fall in vacuum of two objects of unequal mass towards the Earth. Remember that each of these masses exerts a gravitational force UPON THE EARTH, causing the Earth to accelerate towards it. The larger mass will cause the Earth to gain a higher acceleration than the lower, because that acceleration is proportional to the respective masses of the objects, not the mass of the Earth. Thus, the distance between the heavier object and the Earth will shrink faster than the distance between the Earth and the smaller object, i.e, the heavier object, as seen from an Earth-fixed frame will fall faster. This effect is, of course, completely undetectable by today's measuring instruments, and it is impossible to set up an experiment in which the conditions for observerving it would be satisfactorily present, irrespective of measuring instruments (think over why this is so..)
That's brilliant! Does any object with mass have its own gravitational field then? So when I jump in the air there is the gravitaional force of the earth exerted on myself and my own gravitaional force acting upon the earth? My force on the earth must be negligible so really it is not worth taking into account. Or is it?
Yes. Yes, as it should be, according to Newton's 3.law. You don't need to jump in order to bring it into action, though. It's all there, all the time. Nope! The force you exert upon the Earth is equal in magnitude to your own weight, according to Newton's 3. law. Is your weight a negligible force? The force you exert might not be negligible, but the acceleration the Earth gains as a result of being subject to that force is negligible, i.e, the Earth remains practically still.
I understand what you are saying and it sounds ideal. But how about Relativity. If you take into account that when an object goes faster the mass increases towards infinity, then wouldn't the rate be increasing also, since the velocity is related to the mass? Or does special relativity play any such role in gravity.
Is the size of an objects gravitational field in terms of the force it has on other objects reliant on it's mass, so you could have a tiny marble sized planet with a mass greater than all of the planets in that solar system and therefore all those planets will orbit around it. Does size have any relevance in determining to what degree a stars gravitational force is? Could we then say that if the earth was far denser and had a mass twice of what it really is then we would be pulled towards the earth at a greater force?
Indeed. Remember that the magnitude of gravitational field, f(r) set up by a homogenous object of mass M, radius R and r>R, is given by (r and R measured from the object's geometric center): [tex]f(r)=\frac{GM}{r^{2}}[/tex] That is, f varies inversely with the squared distance, and proportionally with the object's mass. Now, when comparing different objects (let's call them stars) and the individual gravitational fields they produce, insofar as their masses are equal and the respective distance are equal then they necessarily must have the same value, irrespective of whether you have a large, diffuse star or a tiny, dense star. As long as the "r" is not less than the R of the largest star, which would violate our condition and place us INSIDE the star, rather than outside. Thus, however you juggle the density and/or volume of your comparison object (yet keeping their product, i.e, mass equal to the other star's) this will in no way affect the gravitational field produced, at distances larger than the greates stars radius.
Great! Thank you, this is Einstein's theory is it now? I imgaine it as like standing on a trampoline in the middle, and if marbles wear able to go around the edge at a constant speed they would in theory orbit around me. Is there any theory on why space bends like this?
Not at all. It is just pure Newton. The world behaves differently in wholly UN-expected ways from this, and Einstein's theory singles out and predicts the effects we may see, for example explaining the anomalous orbiting of Mercury around the Sun, that is anomalous (and hence destructive) of the Newtonian picture. In essence, what is lacking in the Newtonian picture is that time,space and matter are DYNAMICALLY interwoven quantities, for example space becomes warped in the presence of massive objects like a Sun. This means that an underlying assumption of Newton's, namely that space is a Euclidean box in which matter just occupies some portion, is a fundamentally FALSE view of what space "really" is. Relativity, and the real world, is far, far stranger than the picture Newton gave us to believe in; yet it is a damn good picture because mostly, we will experience the world as behaving according to Newton (something that is predictable from Einstein's theory. Of course, for more than mostly, the world behaves according to Einstein).
Not quite sure what you mean by this. Did I say something wrong or is this just a bad interpretation of relativity?
Relativity is a more modern view of physics than Newtonian. Newtonian is more classical. It has nothing to do with Einsteinian theories.
I understand that they are classical and modern. But how can you account for the fact that a mass moving at a velocity weights more? Nobody has given me an explaination of why this is not true.
The concept of relativistic mass is a bit out-dated and leads to confusion, particularly so when it comes to gravitation. I suggest you read the physics FAQ on relativistic mass, link here. From that web page, Although the idea of relativistic mass is not wrong, it often leads to confusion, and is less useful in advanced applications such as quantum field theory and general relativity.