I promised this, so I'll deliver - even though I know it will be dismissed. However the math is here for you to try yourself.
Fist let me point out someone is not doing their math right, and someone using that math is not even bothering to check it. Because these numbers:
Sun Force = 8.872 E13
Earth Force = 3.636 E13
Are pure hokum. Zetetic indeed. See ** at the end.
Now to get on with it...
So, an object in a nearly circular orbit about a mass is neither accelerating toward the mass or away from it, but instead is traveling in more or less uniform velocity around the mass. In other words is exist in a state where at any point on its orbit the force, and therefore the accelerations’ on it are in equilibrium. There are two sources of acceleration, those from gravity and those that arise centrifugally form the orbit itself. Here the task is to show that the accelerations on the moon are in equilibrium. They must all add up to 0. Mathematically stated: ag-ac=0, for each orbital instance.
Let’s use Mr. Rene's facts and figures. According to him we are looking at moon’s orbit around the sun of
r = 1.498E011 m, and a sun’s mass of m=1.991E30 kg
And for the moon’s orbit around earth he gives the following:
r = 4.055E8 m, and an earth’s mass of 5.979E24 kg
He then goes on to calculate something he calls ‘relative force’, there is no such thing, but if we look carefully at the equation he uses:
1) RF = MASS/DISTANCE2, which we can see is similar to the equation for acceleration due to gravity:
2) a = Gm/r2, where G is the gravitational constant (6.67E-11), m is the mass of the object in kg, r the radius of the object’s orbit in meters, and a is the acceleration in m/s2
We are going to need that acceleration. We can get that we can correct Rene’s ‘work’ substituting RF for m/r2 to get:
ag = G*RF
Further, in order to determine the centrifugal acceleration we are also going to need to calculate the orbital velocity of each of these orbits.
3) v = sqrt(Gm/r)
And the centrifugal acceleration, which is given by
4) ac = v2/r
So let’s begin. We will first calculate the accelerations on the sun-moon instance using Rene’s numbers:
ag (sun-moon) = 6.67E-11*1.991E30/(1.498E11)2
ag (sun-moon) = 5.918E-3 m/s2
Now we’ll look at the centrifugal acceleration. Using eq. 3) we get:
v(sun-moon) = sqrt(6.67E-11*1.991E30/1.498E11)
v(sun-moon) = 29774 m/s
Then from eq. 4) we get the centrifugal acceleration as:
ac (sun-moon) = 297742/1.498E11
ac (sun-moon) = 5.918E-3 m/s2
Such that:
ag (sun-moon)- ac (sun-moon) = 5.918E-3 m/s2- 5.918E-3 m/s2 = 0
Well, would you look at that! No net acceleration and hence no net force.
Now let’s now look at the earth-moon instance:
ag (earth-moon) = 6.67E-11*5.979E24/(4.055E08)2
ag (earth-moon) = 2.425E-3 m/s2
Now we’ll look at the centrifugal acceleration as before:
v(earth-moon) = sqrt(6.67E-11*5.979E24/4.055E08)
v(earth-moon) = 991.7 m/s
And the centrifugal acceleration:
ac (earth-moon) = 991.72/4.055E08
ac (earth-moon) = 2.425E-3 m/s2
Such that:
ag (earth-moon)- ac (earth-moon) = 2.425E-3 m/s2- 2.425E-3 m/s2 = 0
My, oh my…
Just as a check on myself, let’s see if the ratio in the gravitational accelerations I calculated for the sun-moon and earth-moon match the ratio given by Rene.
5.918E-3 m/s2/ 2.425E-3 m/s2 = 2.440
Conclusion, there is no net acceleration or force acting on the moon due to the earth or sun.
q.e.d.
**Now just for fun let me note something for those of you that think of Rene as a minor prophet for your FE hypothesis. AS I stated before there is no ‘relative mass’ thingy calculated as m/r2 and further, he mixes his unit systems. In the real world of physics, there are 3 unit systems usually used. cgs/Gaussian (centimeter-gram-second), mks/SI (meter-kilogram-second) and, rarely BE/fsg (foot-slug-second). Your Mr. Rene used kg with km and ended up over estimating his ‘relative force’, whatever that is, by a factor of 1 million!!!! What a cac snámh! And you trust this dude? I will note that in the end he was taking a ratio and since this whole thing is linear in nature the ratio turned out to be correct and I admitted that before – however ignorance + 2 wrongs don’t make a right. The real numbers:
Sun Force = 4.347E20 N
Earth Force = 1.781E20 N
Still a ratio of 2.440, but by doing the real math and producing the real numbers. When you copy a cac snámh, you make yourself a cac snámh. I thought zetetics were not supposed to copy anyone and do the research themselves?