On Nov 23, 11:34 pm, Dr J R Stockton wrote:
In uk.sci.astronomy message 3c047346-7d77-45d8-b8a5-a36b8756047c@g21g20
00hsh.googlegroups.com, Thu, 22 Nov 2007 16:28:09, Weatherlawyer
posted:
The moon weighs some 1/81st the mass of the earth.
...
But they are distinct and do have different speeds. Consider that in
exchange for its capture, the moon travels so much further than us
each year. Whilst the earth is orbiting at some 2Pi x 93 million miles
per year, the moon is in effect orbiting the sun 12 to 13 x 2Pi x
250,000 miles or so further than the earth in that time period.
Nonsense. That is the calculation for both doing a circular 93 Mmi
orbit, and the Moon independently doing 12-13 250 kMi orbits. That is
not what they do. That is like calculating the distance from
Abergavenny to Aberystwyth by adding the distance from Abergavenny to
Ashby-de-la-Zouch to the distance from Ashby-de-la-Zouch to Aberystwyth.
It is easy to show that the Moon's orbit is everywhere concave towards
the Sun, from which it is clear that the annual distance covered by the
Moon is only marginally greater than that covered by the Earth.
To determine said distance, take the vector sum of the Earth's velocity
with respect to the Sun and the Moon's velocity with respect to the
Earth, and integrate for a year.
// Units : Miles, Years. All approximate.
p2 = 2 * Math.PI
EarthSpeed = 93e6 * p2 // wrt Sun
MoonSpeed = 240e3 * p2 * 12 // wrt Earth
Steps = 10000 ; Tot = 0
J = Steps ; while (J--) { T = J/Steps
EarthXSpeed = EarthSpeed * Math.sin(T*p2)
EarthYSpeed = EarthSpeed * Math.cos(T*p2)
MoonXSpeed = MoonSpeed * Math.sin(12*T*p2)
MoonYSpeed = MoonSpeed * Math.cos(12*T*p2)
MoonVelocity = Math.sqrt(
Math.pow(EarthXSpeed+MoonXSpeed, 2) +
Math.pow(EarthYSpeed+MoonYSpeed, 2) )
Tot += MoonVelocity/Steps
}
Tot|0 // output integer part
So Path Length is : 584476336 Miles.
Put Moon distance = 0 : 584336233 " .
Difference : 140103 " - not a lot.
Your answer : 18095574 " - FAR TOO BIG.
The above Javascript was executed in my Web page js-quick.htm. Check
the algebra. Now built into my page gravity3.htm .
--
(c) John Stockton, Surrey, UK. Turnpike v6.05 MIME.
Web URL:http://www.merlyn.demon.co.uk/ - FAQqish topics, acronyms & links;
Astro stuff via astron-1.htm, gravity0.htm ; quotings.htm, pascal.htm, etc.
No Encoding. Quotes before replies. Snip well. Write clearly. Don't Mail News.
Thank friend.
I am relieved that you were not going to involve yourself in tearing
out a crank with ad hominem attacks. It seems to be a favourite
pastime with those who have given up on me.
As for my post, I wasn't getting into astrometry so much as trying to
highlight that the moon makes a lot of effort on our behalf.
Whatever the niceties of the situation, the rolling around of the
months is a bumpy ride and the inertia between all the myriads of
algorithms involved in watching it give us the go-by, leave a little
to be desired of Classical Mechanics.
And it is this difference in acceleration between such huge celestial
objects that sets up the vibes I am trying to discuss. It is I
believe, somewhat similar to the perturbations in satellites observed
over regions such as the Mid Atlantic Ridge.