Expert: Jayendra Upadhye - 6/1/2008

Question
QUESTION: Hi Jayendra,

I'm a little puzzled about the tidal pull of the moon. The pull of the moon on the Earth's Oceans is causing the Earth to rotate slower, which in turn accelerates the moon into a greater orbit(3.8cm/year). This seems wrong to me. More fluid planets like Jupiter must then also be being slowed by their moons which in turn must mean the moons will be accelerating into greater orbits. Has this been observed/measured? And if so by how many cm per year are the  orbits increasing?
Also if the moon is moving away that would mean the barycentre of the Earth and moon is moving away(from the Sun). Is this happening? has it been measured? Is there a more plausible reason why orbits may be increasing?

ANSWER: Robert!
Hold your horses dear fellow!!

You seem to be in great haste or something here...
1 - Jupiter is 1000 times bigger than the earth.
Its mass is approx. 318 times that of the earth.

Of the 63 known moons, 47 are less than 10 km in diameter and can be practically ignored. The others too can be ignored except the largest ones namely, Io, Europa, Ganymede, Callisto.
    Their combined mass is 39.3 * 10 ^ 22 Kilograms.
Jupiter's mass is 1.8986×10^27 kg which is 4831 times bigger!!

The earth /moon ratio for comparison is 5.9736×10^24 kg / 7.3477 * 10^22 kg = (5.9736/7.3477)*100 = 81.3!!

Now you will understand how much more stronger is the influence of the moon on the earth which is only 81.3 times heavier.

The jovian moons have a daunting task ahead of them as their boss is 4831 times heavier.

2 - Angular momentum is effectively transferred from earth to moon due to a strong "coupling effect" namely
a) - Ocean water braking against tidal plains (it is well known where on earth that happens too).
b) - Tidal bulge of the land surface itself. (slight deformation of earth's crust whch is also known to trigger pent up stresses to be released as "early morning" earthquakes).

On jupiter, the thick gas envelop completely discourages this type of "grip" from developing. Surface gravity of jupiter is too strong too, preventing any localised "gas tide" from developing. Worst come to worst, a localised "gas devil" surging towards a "rising moon", as the planet turns (once every 10 hours mind you), will dissipate the enrergy of the coupling as localised "turbulence heat". And cold jupe is an infinite heat sink for such oddities!

So you see, metaphorically it is like a ship (the satellite) dragging an anchor on a sea bottom that is totally smooth and hard! Resulting in "No anchoring".

Since the coupling is weak (only with regard to slowing down of jup and speeding up of the satellites), no appreciable recession results.

However, the coupling is strong enough to periodically elongate the satellites at closest approach and allow them to "snap back" at farthest approach. This results in internal heating of the satellites, phase locking, and extensive volcanism on them.

3 - In the earth moon system, It is the center of mass of the system THAT IS IMMOVABLE!! The recession is for both, and away from their center of mass. the earth is 81 times closer to it than the moon, and recedes 81 times slowly than the moon, from it.

However in the multi-body system of (earth+moon) & sun, The center of mass of the earth+moon system behaves as though nothing is happening, with respect to the sun. (As no work is done with respect to the sun, and Negligible solar differential coupling happens of sun+earth / sun+moon.

It is as if the earth moon center of mass continues "same fashion" all the time, around the sun, but redistributes its mass fractions (moon and earth) a bit farther away from itself in a balanced way.
(like a tight rope walker, the "rope" being the orbit of the center of mass around the sun").

Hope you get it.

Please do rate the answer.

regards
Jayen


---------- FOLLOW-UP ----------

QUESTION: Hi Jayen, I'm also puzzled about the moon's synchronicity. The same side always faces the Earth. But the Gravitational pull of the Sun on the moon is greater than the Earth's pull on the  moon. Why isn't the moon synchronous with the Sun?

ANSWER: Hi Robert!

Hold those horses again!
Something teels me you "make up your mind" first and then 'accuse the world of being conrary'!!

Real science does not work like that.
We have to LEARN NOT to trust our 'beliefs' no matter how 'firm' they are, but be guided entirely by what the calculations say.

Take this case. The sun's pull is almost double compared to that of the earth!

The earth moon distance is 384,403 km.
the earth  sun distance is roughly 147,098,074 km
when moon is between, the moon is closer to the sun by 384,403 km
making moon sun distance = 147,098,074 - 384,403 = 146,713,671 km

Let constant of gravitation be G then
1 - Tidal force on moon due to earth
(actually same force acts on earth too as it is a bidirectional mutual tug)
F1 = [G*(Me)*(Mm)]/(r1*r1)   -   where
F1 = tidal force due to gravitation on moon due to earth
Me = mass of earth
Mm = mass of moon
Likewise
2 - Tidal force on moon due to sun (assume moon midway between the two for worst case)  
F2 = [G*(Ms)*(Mm)]/(r2*r2)   -   where
F2 = tidal force due to gravitation of sun on moon
Ms = mass of sun
Mm = mass of moon
3 - Ratio of force due to earth to that due to sun, on the moon
f1/f2 = (Me/Ms)*(r2*r2)/(r1*r1)

Me/Ms = 0.000003! & (r2*r2)/(r1*r1) = 145669.1651!!

thus f1/f2 = [(5.9736*10^24/1.9891*10^30)]*[(146713671)*(146713671)/(384403*384403)]
     = [0.000003 * 145669.1651]
     = 0.437!! (dimensionless ratio)

Now you will say why the moon does not fall away!
Simple!! (And this is where the mind fools us...The earth is falling too ! (around the sun, along with the moon.

It is like this. The sun is pulling both the moon and the earth with almost double the pull that exists between the two of them (earth moon), but pulling them simultanously. (like a lift falling with a man inside it).

This force is countered by the centrifugal force (a pseudoforce actually, i should be saying centripetal) due to the circular motion of the earth in its orbit.

THAT is why the moon does not fall away. At all times, the tangential velocity component of both earth and moon is sufficient to keep both (their center of mass) in perpetual orbit.

That is given by Fc = Me*Ve*Ve/r2 !
Ve = Orbital circumference / 365.25 days * 24 hrs/day * 3600 sec / hr
  = 2*3.1415*147098074*1000/31557600 met/sec = 29286.675 met/sec
[wikipedia lists it as :-
Average orbital speed 29.783 km/s or 107,218 km/h
we are not quite far off, as we considered perihelion]
Fc then becomes = (5.9736*29286.675*29286.675/147098074*1000) *10^24
  = 34.831 * 10^21 Newton
If you calculate (G*Ms*Me)/(r2*r2) it will match this!
(G*Ms*Me)/(r2*r2) = 6.67*10^-11*5.9736*10^24*1.9891*10^30/(147098074*1000*147098074*1000)
= 36.6272 * 10^21 Newton!
[the 1000s come km to met conversion for mks units].

Our error is (36.6272-34.831)/34.831=5% (again because we took perihelion!

Hope it is clear.
regards

Do rate the answer if you find it meaningful.
Jayen


references:-
1 - http://en.wikipedia.org/wiki/Earth      
2 - http://en.wikipedia.org/wiki/Moon
3 - http://en.wikipedia.org/wiki/Sun


---------- FOLLOW-UP ----------

QUESTION: Hi Again Jayen, I think I get it now. Is it fair to say the Sun pulls on the Earth and Moon as if they are one body.i.e one body between the Earth and moon with the combined masses. And from that the moon is synchronous with Earth because it is the closest large mass to it. I find it interesting that moons are synchronous with their primary and that planets rotate faster than synchronous and seem fastest the further they are from their primary i.e comparing terrestrial planets with Gas Giants. is there a reason for this?

Answer
Hi Robert!
Thanks for the ratings!

However dont you think we aught not to continue a followup with a followup?

These questions are also read by people and the poor guys end up reading the whole bible! For no fault of theirs!

For i DO TEND to write exhaustively.

Coming to your question..
Yes! The sun "looks" only at the center of mass of the earth-moon system. That happens because the gravitationa gradient (of the sun's gravity well) is "almost same" at 93,000,000 miles +/- the eart-hmoon distance.

So both the earth and the moon are perpetually in free fall in a gravitational field (the sun's) that is still doubly stronger than the  mutual earth-moon "pull"! (their tangential velocities are such that the centripetal acceleration equals gravitational attraction by the sun at all times. (constant tangential velocity equalling that of their barycenter).
However superimposed on that is the radial component that describes a simple harmonic motion with a period equalling that of the moon's orbit. That gives the oon its round orbit. Viewed from above the orbital plane (or below), The moon actually describes a cycloidal motion around the sun! (weaving a sanke like pattern with equal throw in the radial direction.

Amongst the terrestrial planets, mars and one of its moons actually present a pair where the moon is spiralling into the planet! As mars speeds up and the moon slows down! In the jovian system too there is such a case.

But this you will have to confirm with a bit of your own research.

Now ..Can we stop this "follow-up business?

You are most welcome to post "fresh questions" ofcourse.

As usual do rate the answer.

regards
Jayen