I’ve been trying to decipher the data types of F, m and a in physicists’ expression F=ma. I still do not know for certain. I believe the standard interpretation by physicists is that force F is proportional to acceleration a

and mass m is the proportionality constant.

**Is force a physical quantity?**

For a proportionality to make sense all its terms must be “physical” quantities. Is F a “physical” quantity? ((It appears that in physics, the definition of “physical quantity” says nothing about the properties of the physical quantity. In physics a physical quantity is a number multiplied by a unit. See this post.)) Was it ever observed and found to be proportional to a? Let’s see. Force in F=ma is an abbreviation for that occult quality that emanates from the sun and travels the earth-sun distance at zero second by breaking all the conservation laws of physics and then sets the earth in motion by instantaneously communicating with the earth’s center about how much of itself to apply to fulfill Newton’s laws and then keeps the earth in orbit accordingly. . .

This is the “physical” quantity physicists made proportional to radius R divided by period T squared, or R/T2.

**Can an occult quality be proportional to a finite distance?**

Only in physics an occult quality that travels the distance R in zero second can be made proportional to the same distance R. ((Is there no limit how far deep into the absurd physicists will push physics in order to save Newton’s authority?))

In this “proportionality” increasing R increases F. So if you double R, F will be twice stronger and the mass m will feel a stronger force the further away it is from the source. I am sure there is a perfectly reasonable “physical” explanation for all this and I’m misunderstanding it all, but mass m feeling or not feeling the force F is a truly academic question. Both F and m cancel. Orbits are independent of F and m.

This “physical” force, physical in the sense that it does not exist in nature but it exists only in physics, does all those fantastic things such as traveling huge distances at zero time yet force cannot be found in the formulas to compute the orbit of the earth.

**Only measurable quantities exist in formulas**

To me if a quantity does not exist in the formulas then it does not govern orbits. And if a quantity has the habit of moving infinitely faster than the speed of light, a sacred speed limit in physics, it cannot be measured with known tools of measurement. Yet physicists claim that “F is proportional to a.”

Force does not hold the orbits together but apparently it holds physics together. Force is the faith of physics.

**F=ma cancels in toto**

So, F is gone. The mass m is gone too. We are left only with acceleration a to describe orbits. No. That’s a goner too because acceleration a stands for R/T2.

Each and every term of the fundamental equation of physics cancel out of the formulas to compute orbits. The terms F, m and a all have type authority. Physicists include them in their equations to save Newton’s authority.

It is true that mass of the earth cancels out of the equation for the orbital motion. The reason for this is the equivalence of inertial mass (mass in the equation F=ma) to gravitational mass, i.e. mass which is the cause of gravity itself (M in F=GMm/r^2)

But you can easily come up with a very simple system that none of the masses cancel out. For example a mass M1 which is free to move up and down attached to another mass M2 with a string (+a pulley) which is free to move in the horizontal direction. Assume there is no friction, then the acceleration (due to gravity) of this system is equal to a = M1*g/(M1+M2). This can be easily measured and the effect of each mass can be identified.

If m is equivalent to M why are you cancelling m in both equations and not M and m? In any case, the definition of force in GMm/r2 says that force is the attraction between matter M and matter m. Now you eliminate m by algebra and associate with your elimination a false “physical” cause. After you eliminate m now force acts between matter M and nothing because m is not there anymore.

This is a good example of how physics is the art of casuistry. When you want it you read M and m as “matter” to say that force acts between two pieces of matter. When you need to eliminate m because you must according to the rules of algebra then you read m as “inertial mass” and M as “gravitiation mass”. And you conveniently forget that you first read them as matter.

Your second paragraph is not about orbits, it is another topic.