Newton's Revised Gravity Theory

[OceanBreeze]

That was the point I was trying to make.  And yes, the standard definition if infinitesimal is vanishingly small but still non-zero.

 

Oh, that was just because you suggested an infinitesimally small force would remain at infinity.

 

I take "infinitesimal" to mean arbitrarily small, but non-zero quantity, on its way to becoming zero in the limit,  but not yet at that limit.

 

To have a non-zero force at infinity would require infinite mass. That is why I prefer to express the situation as one tending to zero as the other tends to infinity. 

 

 

Ah, Ok. Confucius say: Infinite mass at infinite distance can be infinitely confusing.

 

I basically agree with what you are both saying, and at the risk of extending an already silly discussion even further, I will now quote:  Science  Encyclopedias almanacs transcripts and maps  Gravity and the Gravitational Field:

 

"Newton's law of universal gravitation was derived from German mathematician and astronomer Johannes Kepler's (1571–1630) laws of planetary motion, the concept of "action-at-a-distance," and Newton's own laws of motion. Building on Italian astronomer and physicist Galileo Galilei's (1564–1642) observations of falling bodies, Newton asserted that gravity is a universal property of all matter. Although the force of gravity can become infinitesimally small at increasing distances between bodies, all bodies of mass exert gravitational force on each other. Newton extrapolated that the force of gravity (later characterized by the gravitational field) extended to infinity and, in so doing, bound the universe together"

 

 

My reasoning is, if we assume the gravitational field extends to infinity, and that must apply to any mass, large or small, then the gravitational force must also extend to infinity without any need for the mass to be infinite. But this is really more of a philosophical question than physics or mathematics, and maybe interesting to mull over on a rainy day. Certainly not worth arguing about.