Quote:
Originally Posted by bojan
Hmm... this link I provided to Alan only to help defining what we mean by term "spiral", because I think he needed that definition,
Actually so far I do not see we have any disagreement of the issue...
However, this is OT.. the thread is about Alan's "spiral motion" and precession of nodes..
Let's stick to that until the issue it resolved.
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Bojan, thank you for your patience.
Hello bojan,
Here is part two of my explanation of the spiral orbit of Earth about the Sun, producing the precession of the equinoxes, as requested by you. But first, a little of how Newton had to deal with the facts of planetary motion, he had to exercise great care not to openly give recognition to the spiral nature of planetary motion, his whole future could be in jeopardy.
Produced 7 years after Hooke’s death we have Newton’s definition in:
The ‘Principia’. Book 1. The Motion of Bodies, Basic Concepts: Definitions and Axioms.
Definition V
‘Centripetal force is that by which bodies are drawn or impelled, or anyway tend, towards a point as to a centre.
Of this sort is gravity, by which bodies tend to the centre of the Earth; magnetism, by which iron tends to the lodestone; and that force, Whatever it is, by which the planets are continually drawn aside from the rectilinear motions, which otherwise they would pursue, and made to revolve in curvilinear orbits.
………... And the same thing to be understood of all bodies, revolved in any orbits. They all endeavour to recede from the centres of their orbits; and were it not for the opposition of a contrary force which restrains them to, and detains them in their orbit, which I therefore call centripetal, would fly off in right lines, with a uniform motion.
And after the same manner that a projectile, by the force of gravity, may be made to revolve in an orbit, and go round the whole Earth, the Moon also, either by the force of gravity, if it is endued with gravity, or by any other force, that impels it towards the Earth, may be continually drawn aside towards the Earth, out of the rectilinear way which by its innate force it would pursue; and would be made to revolve in the orbit which it now describes; nor could the Moon with out some such force be retained in its orbit. If this force was too small, it would not sufficiently turn the Moon out of a rectilinear course; if it was too great, it would turn it too much, and draw down the Moon from its orbit towards the Earth. It is necessary that the force be of a just quantity, and it belongs to the Mathematicians to find the force that may serve exactly to retain a body in a given orbit with a given velocity; and vica versa to determine the curvilinear way into which a body projected from a given place, with a given velocity, may be made to deviate from its natural rectilinear way, by means of a given force.'
End quote.
Terms from the above we have:
Centripetal force - tending to a centre, = spiral motion.
Of this sort is Gravity, Bodies tending to the centre of the Earth = spiral motion.
Planets continually drawn aside from rectilinear motion = spiral motion
The same of all bodies revolved in any orbits = spiral motion
They all endeavour to recede from the centre = restrained linear motion.
Centripetal = a restraining force, gravity’.
Also,
Moon - retained in its orbit - restrained by some such force not too great and not too small, = a circular orbit.
The latter is an assurance to the governing religious authorities, Moon is not getting closer to Earth.
Newton’s lifesaving statement ; ‘ it belongs to mathematicians to find the force to retain a orbiting body in a given orbit. Very clever, he knew there was no such force, he just passed the buck on.
Newton had side - stepped the issue of perpetual motion implied in retaining an orbiting body in a given orbit.
And who could blame him, or Hooke who had walked away from recognition of spiral motion? They both knew that Gallileo had recanted his works when he was threatened with torture, only 40 years earlier. That is how things were in the 17th century.
Of course, there is more to tell, that was 350 years ago but still today, astronomy kow - tows to the church.
Even so, my faith is in the masters of astronomy right up to Newton and Hooke., who acted within the limits imposed on them during their time. I respect their judgement, they had their necks to lose.
The next step forward for the science of astronomy, in recognising the spiral mode pf planetary motion, will keep for a bit longer it seems.
With this historical background presented, I will explain my view of the cause of the precession of the cause of the equinoxes as requested. It is based on Newton’s explanation and is to my mind, a perfect one, consistent with the law of spiral planetary motion.
His definition is subject to the necessary constraints on him, not to openly recognise the spiral nature of planetary motion, which he dared not venture into. His explanation we recall was delivered in the ‘Principia’. Which we can examine in next post. I will post again soon.
Alan D. 2/11/19
PS I will try to send a graphic that will greatly in my explanation