parsa418
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Does anyone know how Newton knew that the force of attraction between two objects is inversely proportional to the distance between the two objects.
http://en.wikipedia.org/wiki/Isaac_Newtonfter the exchanges with Hooke, Newton worked out a proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector...
If the force is only gravity from the other mass, then the acceleration of the mass is simply the gravity force/mass. The acceleration is the vector sum of the centripetal acceleration and the tangential acceleration. If it is circular motion with no tangential acceleration and M1>>M2:parsa418 said:Thank you this is making a lot more sense now. I only have one remaining question:
How is the centripetal force related to the attracting forces between the two objects. I mean these objects aren't rotating each other or anything? are they?
parsa418 said:Two Questions:
Could you prove why the period squared equals to the radius cubed
and do all objects rotate around each other?
Bill_K said:You only need Kepler's Third Law, "The period squared goes as the radius cubed."
T2 = (2πr/v)2 ~ r3 shows that v ~ r-½. Then the centripetal force required is F = mv2/r ~ 1/r2
ank160 said:But how did Kepler derived that T^2 is proportional to r^3.
ank160 said:But how did Kepler derived that T^2 is proportional to r^3.
There is no "proof". One does not prove things in science like one does in math. Science is only as good as the evidence that supports it.parsa418 said:Hi
Could anyone please tell me how did Newton prove that the force of attraction between two objects is inversely proportional to the distance between them squared. I know that if you use Kepler's law that the T^2=r^3 you could prove it. However, I still don't get how kepler proved that T^2=R^3. A lot of people told me it was based on observations. But I know there has to be some proof for this observation by now. Please give me a full proof of this matter.
Thank you
Vagn said:He didn't, he observed them.He was Tycho Brahe's student and had access to Brahe's catalogues which where extremely accurate with over a decades worth of data. This allowed him to use the data to empirically show his laws to be true.
parsa418 said:Then how did Newton exactly observe this. I mean there weren't any force sensors at the time or was there something like it?
Newton postulated that the force of gravity provided the centripetal acceleration that could be calculated from the observed data.parsa418 said:Then how did Newton exactly observe this. I mean there weren't any force sensors at the time or was there something like it?