So, you agree that as the object is changing its orbital radius, "Energy either has to be added to the orbit or lost from it"
That is a key element. It proves that there is no conservation of energy in the total rotation energy
You have it backwards. An object won't change its orbital radius unless it is gaining energy from an outside source or losing it to an outside source. A spacecraft won't spontaneously increase its orbital radius from the Earth, for example. If the astronauts want to increase the orbital radius, they will have to add energy by firing the engines.
If you mean that there is a conservation of energy after adding new energy - that is fully clear.
But again - There is no conservation of energy in the total rotation energy!
Since energy is neither created nor destroyed, yes there is.
So, we fully agree that once you change the radius you need to add energy or decrease energy.
Again, you have it backwards. Adding energy from an outside source will increase the orbital radius. You can't say, "I want the orbital radius to increase, so the energy required to do that pops up out of nowhere". The radius won't increase unless the object in orbit is supplied with energy from another source that already existed. Look at my example with the spaceship.
If you add or decrease an energy to or from the total energy - than how can you still think that the total energy remains the same?
Because the energy lost by the black hole's spin is now present in the particles it created. The total energy (black hole + particles) is the same.
Do you agree that based on this idea, in order to decrease an energy of the total rotation energy, the black hole's spin rotation should be increased?
That is the exact opposite of what would happen. Decreasing the black hole's rotational kinetic energy causes the spin to be slowed down.
In any case, you claim for a direct linkage between the Total rotation energy of the orbital object around the main body, to the spin of the main body.
That depends on what you're talking about. When you say "total rotation energy" are you talking about the total orbital energy or what?
If you set there one billion objects that orbits clockwise or the other side - do you agree that all of them will fully obey to Newton law whithout any ability for the moon to transfer even one bit of its spin energy (especially not to the one of the orbital direction). So the moon's spin would continue to rotate at the same fixed velocity while all the Billion objects will fully obey to Newton law and orbital velocity whithout getting any extra energy from the Moon's spin.
You would actually expect the opposite to occur. Instead of the objects in orbit being given energy by the Moon's spin, you'd expect them to transfer energy to the Moon and spin it up instead. That's because they would be orbiting the Moon faster than the Moon rotates. If the opposite was true and the Moon was spinning faster than the orbit, then you would expect the Moon the slow down while raising the orbital radius of the object
Hence, there is virtually no ability for any real energy transformation from the Moon spin to the requested orbital objects.
Therefore, If the moon doesn't transfer any energy from its spin velocity to any orbital object (while it's Kinetic energy + potential energy will fully obey to Newton law) - could it be that even the SMBH won't need to transfer any energy from its spin velocity?
This is a completely ridiculous conclusion. You are basically arguing, "Objects that don't spin can't transfer spin energy, therefore spinning objects don't transfer spin energy either." That's like arguing that a car without gas in its tank can't run therefore a car with gas in its tank can't run either. Spin is the very thing that makes these two scenarios different.
Please - So far you couldn't offer any real formula (By Newton or Einstein) that directly links the spin energy/velocity of the main body to the orbital energy of the orbital object.
If you are talking about finding the rate of energy transfer over time, you would need to use multiple equations to figure that out. They are listed on this page: https://en.wikipedia.org/wiki/Tidal_acceleration#Theory
It's a much simpler matter if you are asking how much spin energy is required to increase the orbital radius by a given amount. First you would calculate the increase in total orbital energy when going from the old radius to the new radius (using the orbital kinetic and potential energy equations). Then you subtract that resulting energy difference from the total rotational kinetic energy of the primary body. You can then use the rotational kinetic energy equation to calculate how much the primary body's spin should have slowed down.
I have a question for you:
Why are you so sure that "an increase in the orbital radius requires a net input of energy"?
Because the law of conservation of energy demands it. Energy doesn't pop up out of nowhere.
Therefore, an increase in the orbital radius requires less and less input of energy.
Yes, but that input of energy is still non-zero at all distances. That's the important part.
However, it seems to me that there is a rang limit for that potential energy.
Yes, potential energy reaches its maximum (and finite) value at infinity.
However, if the object is too far away from the Earth or even from the sun, the gravity force is decreasing dramatically and I wonder what is the real meaning of the potential energy while the gravity force is almost gone to zero.
It still has the same meaning. Just because the gravity is weak doesn't mean it isn't there. The math still works.
I'm not fully sure about it, but it seems to me that for any orbital system up to a certain radius - we can claim for sure that: "an increase in the orbital radius requires a net input of energy.
It works for all radii because gravity has infinite range.
Now, we know for sure that the Oort cloud is drifting outwards constantly.
So, without any need for external energy - those objects at Oort cloud are increasing their radius over time.
Given that the Oort cloud is theoretical at this point, I'm going to have to ask you to cite an authoritative source that supports your assertion that the cloud as a whole is drifting away from the Sun (if it exists).
1. Is it a Normal activity at gravity that too far away orbital objects are drifting outwards over time?
No, although it is easier for such objects to be dislodged from their orbits by even tiny amounts of energy contributed from other sources. Impacts from asteroids or gravitational tugging from other objects in the vicinity are possible sources of such energy.
2. Could it be that the gravity force is decreasing over time for orbital objects that are located too far away?
Due to the gravitational constant, no.
3. How can we find that radius range that converts the " an increase in the orbital radius requires a net input of energy" to "an increase in the orbital radius over time requires no net input of energy - It is a normal activity of Gravity force"?
You can't, because it doesn't exist.
4. Could it be that this range is set by finding the radius when The Kinetic energy is equal to potential energy?
In other words - if Kinetic energy is greater than Potential energy - an increase in the orbital radius requires a net input of energy, however if the potential energy is greater that the kinetic energy than " an increase in the orbital radius over time requires no net input of energy"?