A Matter Of Curvature.

Thinking about a spaceship orbiting Earth as being a balance between the gravitational force on it and the inertial force resulting from the ship’s constant change of direction it occurred to me that all bodies in a stable, circular, orbit would be ‘weightless’ in respect to the thing they were orbiting.

From this it seems likely that as we are in orbit around the sun we are ‘weightless’ as regards its gravitational attraction, as in fact would all the planets be and hence they would feel their own gravity unaffected by that of the sun.

Pondering why the planets velocity around the sun did not decrease with the square of the distance to the sun it occurred to me that it is because orbits are a balance between the gravitational attraction of their sun and the amount of inertia caused by the path of the planet - in other words it is a matter of balancing curves. When the curve of the orbit matches the curve of gravity then the planet is in orbit.

Since the curve of gravity depends on the distance to the sun and the curve of the planet depends on its orbital speed then a body that is travelling too slow will fall and a body that is travelling too fast will ‘rise’.

In a way it is a battle between the straight line and the curve as the planet wants to move in a straight line but it is forced to curve by gravity.
The strength of the gravitational field simply results in varying scales, presuming that the inertia of curving remains constant, since a circle is a circle is a circle.

I suppose that I ought to explain why going faster takes the planet ‘higher’ (further from the sun) even though the orbital speed of planets drops as you go ‘higher’…

The crucial factor is that the strength of the gravitational pull must be strong enough to ‘fit’ the curve that the orbital body is describing with that of a circle at that distance from the sun.
In other words if its speed is too great for the pull of gravity (at that distance from the sun) to curve it enough then it will move outward and if its speed is too low then it will curve too much and start to move closer to the sun.

Naturally, this is only true for a circular orbit but for other orbits it is similar but with inertial dances of acceleration caused by variations in the balance between the inertia of nucleuses of the atoms and the direction of the inertial frame they compose as the orbit the sun...

As I’ve pointed out elsewhere the Wall Of Death (in which a motorbike circles a vertical wall) is much the same principle except the wall forces the motorbike to curve around the circle rather than gravity.
In both cases it is the inertia of curving that supplies the force to counteract gravity and yet it seems difficult to see how curved space might be involved in the Wall Of Death.

Certainly the fact that gravity pulls from a central point does give an effect that appears to be curved but it may well be that it has little to do with space beyond the fact that it diminishes with distance.

Kepler’s second law - The Law Of Areas - tells us that, due to the conservation of angular momentum, a line that connects a planet to the sun (essentially the planet’s varying orbital radius) sweeps out equal areas in equal times.

In other words that the relationship between distance from the sun and gravitational force is a result of the inverse square law of gravity.
So, in theory, at twice the distance the force should be quartered yet the orbital velocity remains higher than expected.

The Earth's mean orbital velocity is almost 30 Km/s yet Neptune which is over 30 times more distant from the sun still manages almost 5.5 Km/s despite the force of gravity being some 900 times weaker.

Checking using Kepler’s Third Law.
Since Neptune is approx 30 times as far from the sun as the Earth then it must traverse 30 times the distance and it turns out it travels at approx 5.5 times slower than the Earth so it takes approx 30x5.5 = 165 years.

The actual figure is about 164.8 so it is close enough for me. Yet I'm still staggered that Neptune can orbit the sun at over 1/6 of the velocity of the Earth on 1/900th of the gravitational force that the Earth gets!

Having checked Kepler’s laws if there is a mistake it must be in Isaac Newton’s assumption that gravity follows the inverse square law.
I'll give it some thought...

centripetal acceleration = v squared / radius
for the Earth 29.79 squared = 887.44/1 (AU)
for Neptune 5.43 squared = 29.48/30.6 (AU)
giving 887.44 to 0.963. close enough to 900 to 1...
(but interestingly multiply instead of dividing gives 887.44 to 902...

Ah, setting the Earth’s distance from the sun as unity (1 AU) has set the square of the Earth’s velocity as the value of the square of the orbital velocity times the distance from the sun for all the planets!

It might be interesting to set an imaginary planet with a distance from the sun as 1 light second - or maybe a light minute.
1 AU is about 500 light seconds so perhaps an imaginary planet at 8 light minutes might work well.

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I've played with an imaginary planet using C as the basic unit of length ie Light Seconds and it is starting to look as if Newton was almost right but he was trying to solve a three dimensional problem in two dimensions.

It seems to me that I was close with my concept of it being a battle between the curve and the straight line but like Newton I was thinking in two dimensions.

I'm not well at the moment but as soon as I feel better I will consider if could be a battle between the cube and the sphere and if gravity could be a consequence which might well explain the connection of curve doubling with the square root of eight.

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What really interest me is whether the inertia of curving is constant or not - does it require more force to produce identical curves (i.e. to turn through an identical angle while travelling an equal distance) when it is closer to the gravitational source than it does when it is further away?

Although it might seem simple to check this out I’m not sure how anything in space can control its rate of curving at two separate distances from the sun without changes in its acceleration - can you think of a means of doing it?

I think I must be suffering from the Davro effect* because of course the LHC is exactly what is needed to test if the force needed to ‘bend’ things around a curve is always proportional to the speed of the thing being bent ;O)

What the LHC does is force things to bend ever faster around the same curve.

So is there any discrepancies in a comparison between the results taken from a linear accelerator and that of the LHC?

If I’m right then the extra effort needed to curve would add an increasingly large increment to the force needed to attain the same linear speed.

Certainly it will make a huge difference to the results once the LHC swaps to using iron and I must say I have trepidations about what effect the LHC might have once it does - due to the dramatical increase in inertia.

Makes you wonder if Einstein was thinking about the inertia of curving when he said that as a thing approached the speed of light its mass approached infinity - perhaps he was calculating the increasing effect of inertia when accelerating through curved space.

It is worth bearing in mind that a straight line is a quite probably a hypothetical concept in a curved Universe or even in a Universe where the effects of gravity are ubiquitous.

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When I wrote earlier that the Earth should show little or no gravitational effect from the sun (obviously it supplies the gravitational attraction to keep the Earth in orbit) I had considered the Moon as simply that, a moon, but on checking I found that although the Earth/Moon centre of gravity lies within the Earth) that, to some extent, they dance like partners as they circle the sun - with the Earth, the heavy partner, swinging the dainty Moon around it but both revolving around their common centre.

Without doubt that must alter the effect the sun’s gravity has on the Earth.
It seems that the Sun is 391 times as far away from the Earth as the Moon but its force on the Earth is about 175 times as large and yet its actual tidal influence is less than 45% of that of the Moon.

This is explained by the fact that being nearer the moon's gravity has a wider effect on the earth - it is obviously presumed that because gravity, like light, follows the inverse square law that its ‘gravitational rays’ must also act like light rays.

Strangely, the same reasoning is followed for the Land Tides and yet it is even more obviously unlikely since you would expect a force that is 175 times larger yet concentrated into a smaller area to show a much larger and not smaller effect on solid land!

Because of the Moon's dance with the Earth affecting the earth's orbit I have no reason to argue with the belief that the sun’s gravitational effect on the Earth is less than half that of the moon but I can’t say I believe the commonly accepted reason for that.

* http://www.abctales.com/story/terrence-oblong/observation-many-people-bo...