Expert: Jayendra Upadhye - 8/3/2005

Question
I have read that the moon and the earth are getting further apart by approx 4cms a year. Considering that the moon's gravitational pull is strong enough to effect tides here on Earth and that Earth's gravitational pull is strong enough to keep the moon in orbit, Why don't the Earth and Moon come closer together rather than further apart?  

Answer
Hi,
Interesting question.
Chris, first of all remove from your mind the idea (it took me 30 years) that anything that causes tides in the oceans indicates a "very strong" gravitational pull.

The oceans constitute a large body of liquid, and under uniform and wide "small pulls", this water body can accumulate into a large tidal bulge!

For example, the sun exerts a "g" force of a very small magnitude on the earth. But it still causes the solar tides.

eqn 1 :-
g = square of the orbital velocity / orbital radius.

this is a consequence of uniform circular motion where centripetal acceleration (here due to gravity) equals v^2/r.

for the earthm V = (2*pi * 93 million miles * 1.6 km/mile) / (365.25 days * 24 hrs/day * 3600 sec/hr) = 29.626 km/sec roughly.

That corresponds to a g (due to sun) = (29.626 *1000 squared) met-squared/sec / (93000000 miles * 1.6 km/mile * 1000 met/km)
or g = 0.00589 met/sec/sec ! (approx 0.006 met per sec aquared!).

And that is enough to swing the earth around in its orbit and give us "mighty" solar tides!

Refer the moon facts at the site :-
http://home.hiwaay.net/~krcool/Astro/moon/moonpedia/
the GM value for the moon is 0.0049 * 100000 km cubed/sec squared.

its mean orbital radius (semimajor axis) = 0.3844 * 1000000 km = 384400 km. giving an earth surface to moon distance of 384400 - mean earth radius.
mean earth radius = 6371 km as per site :- http://whatis.techtarget.com/gDefinition/0,294236,sid44_gci816253,00.html

Thus earth surface to moon center distance is 378029 km.
yielding g value (due to moon) at distance to earth's surface

g(moon) = GM of moon / distance to earth's surface squared.
g(moon) = GM for moon/ (378029) squared in km units or
g(moon) = (0.0049*100000)/(378029*378029)   units are [km cubed / sec squared] / [km squared] = [km/sec squared]

this lunar g at earth's surface = 3.4288 * 10^-9 km/sec squared.
or g(moon) = 3.4288 * 10^-6 m/sec squared !

That is 0.05% that of the sun!

So much for tides!

The lunar recession rate (annual) is listed 3.8 cm/sec on that moon site.

This is so because of the tidal coupling of the moon and earth by gravity.

Even though the "pulls" are small, the tides slow down the rotation of the earth on its axis by "braking" action of the surf on land and swells on the ocean bed.

This slow down constitutes a "change in angular momentum of the earth.

By law of conservation of angular momentun, the moon (the cause of braking) is speeded up in its orbit.

As it gains kinetic energy at the expense of earth's stored rotary energy, it converts the same into additional hieght (increasing its store of potential energy).

This is seen as a spiralling away, as this increment is slow but steady and continuous!

As it recedes, it's gravitational pull will weaken, and braking will also weaken, till it becomes infintesimally small, and it stops receding for all practical purposes. That distance will be a sort of "barrier" beyond which it will "never go".

I do not know what that distance might be, but it will be awfully great!

Last but not the least..
If you find the time, read asimov's "last question" on the web. One guy asks a large computer whether entropy can be reversed. ofcourse the computer says "insufficient data for a meaningful answer". A million years pass, and another asks a more advanced computer the same question and gets the same answer.

billions of years later the universe fades away..a computer in hyperspace has all the answers except one asked it by a human billions of years ago.

An eternity passes in empty dead space when suddenly the computer finds the answer.
In a language utterly incomprehensible to anything "living" it says the equivalent of "let there be light" and the universe starts all over gain !


pls do rate this answer if it has helped you in any way.
Jayen