Change in lunar revolution period

Hi all,
It's understood that the moon is slowly receeding from the Earth at a
rate of about 3.82 cm/year. This is pretty small, but over millions of
years, it really adds up. Around the time of the dinosaurs, the moon
was something like 9,000 kilometers closer to Earth than it is today.
Still, not too much (like a 2% change or something), but still a
noticeable one.

My question: Was the lunar revolution period smaller when it was closer
to Earth, or has it slowed it's velocity as it has retreated for no net
effect? If it's still moving at the same velocity as it was 200 million
years ago, that would mean it would have cycled the Earth faster than
it does now (because it would be moving around in a smaller radius),
probably to a period of like 25 days instead of 27 like it is now. Is
this true? Does anyone know the math behind this, to know exactly how
the period of revolution changes as the moon receeds?

"Navillus" wrote in message
oups.com...
Hi all,
It's understood that the moon is slowly receeding from the Earth at a
rate of about 3.82 cm/year. This is pretty small, but over millions of
years, it really adds up. Around the time of the dinosaurs, the moon
was something like 9,000 kilometers closer to Earth than it is today.
Still, not too much (like a 2% change or something), but still a
noticeable one.

My question: Was the lunar revolution period smaller when it was closer
to Earth, or has it slowed it's velocity as it has retreated for no net
effect? If it's still moving at the same velocity as it was 200 million
years ago, that would mean it would have cycled the Earth faster than
it does now (because it would be moving around in a smaller radius),
probably to a period of like 25 days instead of 27 like it is now. Is
this true? Does anyone know the math behind this, to know exactly how
the period of revolution changes as the moon receeds?

http://www.geo.umass.edu/courses/geo892/moon_orbit.pdf

Maybe this can help you.

George

On 10 Apr 2006 01:27:42 -0700, "Navillus"
wrote:

My question: Was the lunar revolution period smaller when it was closer
to Earth, or has it slowed it's velocity as it has retreated for no net
effect? If it's still moving at the same velocity as it was 200 million
years ago, that would mean it would have cycled the Earth faster than
it does now (because it would be moving around in a smaller radius),
probably to a period of like 25 days instead of 27 like it is now. Is
this true? Does anyone know the math behind this, to know exactly how
the period of revolution changes as the moon receeds?

Apply Kepler's third law: the square of the period is proportional to
the cube of the semimajor radius of the orbit.

William Hamblen wrote:
On 10 Apr 2006 01:27:42 -0700, "Navillus"
wrote:


My question: Was the lunar revolution period smaller when it was closer
to Earth, or has it slowed it's velocity as it has retreated for no net
effect? If it's still moving at the same velocity as it was 200 million
years ago, that would mean it would have cycled the Earth faster than
it does now (because it would be moving around in a smaller radius),
probably to a period of like 25 days instead of 27 like it is now. Is
this true? Does anyone know the math behind this, to know exactly how
the period of revolution changes as the moon receeds?


Apply Kepler's third law: the square of the period is proportional to
the cube of the semimajor radius of the orbit.



Kepler's third law (the square of the orbital period is proportional to
the cube of the semimajor axis) holds as William Hamblen point out.

Newton discovered (and showed mathematically) that objects in free fall
(such as planets influenced by a central force like the Sun's gravity)
follow the paths of conic sections.

The task of deducing all three of Kepler's laws from Newton's universal
law of gravitation is known as the Kepler problem. Its solution is one
of the crowning achievements of Western thought.

Isaac Newton's solution to "the Kepler Problem" is well presented in
episode 22 of "The Mechanical Universe" series, mathematics and all and
can be viewed online at

http://www.learner.org/resources/series42.html

Navillus asked:
...Was the lunar revolution period smaller when it was closer
to Earth, or has it slowed it's velocity as it has retreated for no net
effect?

William Hamblen replied:
Apply Kepler's third law: the square of the period is proportional to
the cube of the semimajor radius of the orbit.

Sam Wormley replied:

Kepler's third law (the square of the orbital period is proportional to
the cube of the semimajor axis) holds as William Hamblen point out.

Newton discovered (and showed mathematically)...

The task of deducing all three of Kepler's laws from Newton's universal
law of gravitation is known as...

Isaac Newton's solution to "the Kepler Problem" is well presented in
episode 22 of...

I'm wondering if a "yes" or "no" might have sufficed for the /first/
part of Navillus's question? That way those of us who stayed up until
three A.M. in our observatories, and who have two acres of lawn to cut
and 56 acres of winter cover to plow-under today, but lack the skill to
operate a slide rule while driving a tractor, would also know the
answer.

Thanks.

Davoud

--
usenet *at* davidillig *dawt* com

Davoud wrote:
Navillus asked:
...Was the lunar revolution period smaller when it was closer
to Earth, or has it slowed it's velocity as it has retreated for no net
effect?

William Hamblen replied:
Apply Kepler's third law: the square of the period is proportional to
the cube of the semimajor radius of the orbit.

Sam Wormley replied:

Kepler's third law (the square of the orbital period is proportional to
the cube of the semimajor axis) holds as William Hamblen point out.

Newton discovered (and showed mathematically)...

The task of deducing all three of Kepler's laws from Newton's universal
law of gravitation is known as...

Isaac Newton's solution to "the Kepler Problem" is well presented in
episode 22 of...

I'm wondering if a "yes" or "no" might have sufficed for the /first/
part of Navillus's question? That way those of us who stayed up until
three A.M. in our observatories, and who have two acres of lawn to cut
and 56 acres of winter cover to plow-under today, but lack the skill to
operate a slide rule while driving a tractor, would also know the
answer.

Thanks.

Davoud

--
usenet *at* davidillig *dawt* com

Very cool article. Thanks for posting the link. To supplement, here's
some info-light links on the same topic at Ask-an-Astronomer and the
Astronomy Cafe.

Is the Moon moving away from the Earth? When was this discovered?
http://curious.astro.cornell.edu/que...php?number=124

Did the Earth rotate faster in the past?
http://www.astronomycafe.net/qadir/q395.html

Will we ever stop having solar eclipses because of the moon's motion
away from the Earth?
http://curious.astro.cornell.edu/que...php?number=294

Is the Moon moving away from the Earth?
http://www.astronomycafe.net/qadir/q1282.html

Will the Moon be invisible in 500 million years?
http://curious.astro.cornell.edu/que...php?number=579

- Canopus56

Navillus wrote:
My question: Was the lunar revolution period smaller when it was closer
to Earth, or has it slowed it's velocity as it has retreated for no net
effect?

I'm not sure what you meant to ask here, but both are true. The lunar
revolution period *was* shorter then than it is now, and it has been
getting longer as the orbit gets larger. What's more, the period gets
longer at a greater rate than the orbit gets larger, so the Moon is also
becoming slower, to boot.

People have mentioned Kepler's third law of planetary motion. That
states that the square of an object's period varies in direct proportion
to the cube of its average distance from what it orbits. Kepler meant
it to apply to the Sun and the different planets, but it works equally
well in connection with the Earth and the Moon--where instead of taking
different planets, we take the same object (the Moon), but at two
distinct times in its history.

So, if long ago, the Moon's distance from us was, say, 0.8 times as far
as it is now, we can take the cube of that and get 0.512. Then the
square of the orbital period (compared with its period now) would equal
0.512, also. That gives us about 0.72, so that the month would have
lasted a bit less than three-fourths of what it does now.

The actual orbited distance, of course, is proportional to the Moon's
distance from us, so in that long ago time, the Moon travelled 0.8 times
the distance that it does now, in 0.72 times the time that it takes now;
that is to say, it was moving faster than it does now, by about 10
percent.

--
Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html

William Hamblen wrote:
On 10 Apr 2006 01:27:42 -0700, "Navillus"
wrote:

My question: Was the lunar revolution period smaller when it was closer
to Earth, or has it slowed it's velocity as it has retreated for no net
effect? If it's still moving at the same velocity as it was 200 million
years ago, that would mean it would have cycled the Earth faster than
it does now (because it would be moving around in a smaller radius),
probably to a period of like 25 days instead of 27 like it is now. Is
this true? Does anyone know the math behind this, to know exactly how
the period of revolution changes as the moon receeds?

Apply Kepler's third law: the square of the period is proportional to
the cube of the semimajor radius of the orbit.

I'm having trouble with this... qualitatively speaking, when the moon
was closer to the Earth, it completed each full period in less time
than it takes today, correct?

So, in the distant past the Moon was both closer and orbited the Earth
faster.

BUT, was it tidal locked in terms of always facing one side towards the
Earth as it orbited and if not what was the diference in terms of orbit
vs roatation?


A second, related but diverging, question:

How stable might a pair of Earths be if they were co-joined in a
binary obit around the Sun?


TBerk