[Kryptid]

Sorry Kryptid, but I'm actually with sorlov on this one.  The two forces are equal and opposite, one acting on the planet (thus slowing it down on its way out to aphelion), and the other acting on the primary (star presumably), slowing it down as well. The planet slows down not because the forces are not equal, but because the force is not acting tangentially to its motion.

I realize (due to Newton's third law), that the gravitational force on the planet must be equal and opposite to the gravitational force on the Sun. Likewise, the centrifugal force on the planet and the Sun must also be equal and opposite. But must this mean that the gravitational force between the Sun and planet are always equal to the centrifugal force between the Sun and planet? How can the planet and Sun accelerate away from each other if there is no net force present between them? F=ma seems to demand a net force in order for an acceleration to be present.

[Halc]

I realize (due to Newton's third law), that the gravitational force on the planet must be equal and opposite to the gravitational force on the Sun. Likewise, the centrifugal force on the planet and the Sun must also be equal and opposite. But must this mean that the gravitational force between the Sun and planet are always equal to the centrifugal force between the Sun and planet?

There is an equal and opposite force, per Newtons 3rd law. You can call it a centrifugal force if you like, but I never thought that made sense in any but a rotating frame. It's just a force of gravity, one mass acting on another, each accelerating the other.

How can the planet and Sun accelerate away from each other if there is no net force present between them?

They never accelerate away from each other.  Acceleration vector is always straight towards the other in a 2 body system.  They move away from each other (by inertia), but since they're slowing down while doing that, they're not accelerating that way.

F=ma seems to demand a net force in order for an acceleration to be present.

There is a net force on each mass, hence each of them accelerates.  If there is a string, tension on that string represents the one force accelerating each object.  The system as a whole has balanced forces and the center of gravity of that system is thus entirely inertial (non accelerating).

[sorlov (OP)]

Ravenstvo tsentrobezhnykh i tsentrostremitel'nykh (gravitatsionnykh) sil bylo tem "yablokom, kotoroye upalo na golovu N'yutona". Krome etogo ravenstva, on znal rezul'taty issledovaniya Keplera - zakon obratnogo kvadrata. Poetomu on legko iz etikh dvukh zakonov uznal zakonomernost' ubyvaniya sily gravitatsii - obratno proportsional'no kvadratu udaleniya -  1/r  v kvadrate. Eto byl i yest' yedinstvennyy obosnovanyy chlen v yego uravnenii vsemirnoy gravitatsii. Vse ostal'nyye - lozhnyye ili empiricheskiye. Oni uvodyat uchonykh v lozhnuyu storonu.
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The equality of centrifugal and centripetal (gravitational) forces was the "apple that fell on Newton's head." In addition to this equality, he knew the results of Kepler's study - the law of the inverse square. Therefore, he easily learned from these two laws the pattern of decrease in the force of gravity - inversely proportional to the square of removal - 1 / r squared. This was and is the only valid term in his equation of universal gravity. All others are false or empirical. They lead scientists in a false direction.

[sorlov (OP)]

Это просто сила тяжести, одна масса действует на другую, каждая ускоряет другую.

Unfortunately, you did not understand my theory. No body attracts to itself. The ethereal vortex performs the force of attraction, more precisely, the pressure gradient in it, which increases towards the center of this vortex. No need to repeat the unproven fantasies of Newton or Einstein. I proved my theory, as mentioned above.

[Halc]

It's just a force of gravity, one mass acting on another, each accelerating the other.

Unfortunately, you did not understand my theory. I wasn't commenting on your theory. I was replying to Kryptid.

I pretty much dropped out of the conversation after pointing out a substantial list of claims contradicting empirical evidence, such as Pluto not having moons for instance.