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Effect of Moon's Gravity on Earth



 
 
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  #1  
Old March 23rd 04, 04:19 PM
Gordon D. Pusch
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Default Effect of Moon's Gravity on Earth

"Cockpit Colin" writes:

"If the gravity of the moon can, from a quarter of a million km away, be
strong enough to influence millions of tons of water (ie tides), would it be
able to cause any apparant variation in a person's weight here on earth"

Reason I ask is that at the moment I'm weighing myself daily - and I'm on a
diet that's VERY consistent - and yet I often get variations on my
(electronic) scales of up to 2 pounds / 1kg from day to day (even though I'm
averaging several readings) - and was wondering if the moons gravity might
be strong enough to induce even so much as a 1% error?


No. Gravity obeys an inverse square law, i.e., doubling the distance
decreases the strength of the "gravitation force" by a factor of four,
tripling the distance decreases it by a factor of nine, etc. Rounding
all figures to one significant digit to make them useless in case this
is really a homework problem and not a question of mere idle curiosity,
the Moon has a radius of a bit under 2000 km, and a mean distance of a bit
under 400,000 km (neglecting the radius of the Earth, which is unimportant
on this scale). Since the Moon is over 200 times farther than its radius,
by the inverse square law its gravitation force, already only 1/6 that of
Earth at its surface, would be reduced by a another factor of over 40,000,
to less than one part in 200,000. This is many MANY times smaller than
"one part in 100," which is what "1%" means.

The above should be sufficient to answer your question if it is merely
due to curiosity. If it is homework, you will need to look up the actual
numbers and work out the answer for yourself.


-- Gordon D. Pusch

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  #2  
Old March 24th 04, 03:19 PM
Dr John Stockton
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Posts: n/a
Default Effect of Moon's Gravity on Earth

JRS: In article , seen in
news:sci.space.science, Gordon D. Pusch [email protected]
et.com posted at Tue, 23 Mar 2004 10:19:14 :-
"Cockpit Colin" writes:

"If the gravity of the moon can, from a quarter of a million km away, be
strong enough to influence millions of tons of water (ie tides), would it be
able to cause any apparant variation in a person's weight here on earth"


Not a quarter of a million km.

Reason I ask is that at the moment I'm weighing myself daily - and I'm on a
diet that's VERY consistent - and yet I often get variations on my
(electronic) scales of up to 2 pounds / 1kg from day to day (even though I'm
averaging several readings) - and was wondering if the moons gravity might
be strong enough to induce even so much as a 1% error?


No. Gravity obeys an inverse square law, i.e., doubling the distance
decreases the strength of the "gravitation force" by a factor of four,
tripling the distance decreases it by a factor of nine, etc. Rounding
all figures to one significant digit to make them useless in case this
is really a homework problem and not a question of mere idle curiosity,
the Moon has a radius of a bit under 2000 km, and a mean distance of a bit
under 400,000 km (neglecting the radius of the Earth, which is unimportant
on this scale). Since the Moon is over 200 times farther than its radius,
by the inverse square law its gravitation force, already only 1/6 that of
Earth at its surface, would be reduced by a another factor of over 40,000,
to less than one part in 200,000. This is many MANY times smaller than
"one part in 100," which is what "1%" means.

The above should be sufficient to answer your question if it is merely
due to curiosity. If it is homework, you will need to look up the actual
numbers and work out the answer for yourself.


Correct result, but incorrect reasoning.

The Moon does attract a person underneath it, but it also attracts the
Earth. One needs to calculate, therefore, not the pull but the
differential pull; the variation of the lunar gravitational field over
the 4000 miles that separate the centre of a person from the centre of
the Earth.

The effect will therefore be much less than you calculate; by a factor
of the order of (Moon's distance / Earth's radius), which is about 60,
and perhaps another factor of the order of unity.

--
John Stockton, Surrey, UK. /
Web URL:http://www.merlyn.demon.co.uk/ - FAQish topics, acronyms, & links.
Correct = 4-line sig. separator as above, a line precisely "-- " (SoRFC1036)
Do not Mail News to me. Before a reply, quote with "" or " " (SoRFC1036)
  #3  
Old April 2nd 04, 09:00 PM
rick++
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Posts: n/a
Default Effect of Moon's Gravity on Earth

Reason I ask is that at the moment I'm weighing myself daily - and I'm on a
diet that's VERY consistent - and yet I often get variations on my
(electronic) scales of up to 2 pounds / 1kg from day to day (even though I'm
averaging several readings) - and was wondering if the moons gravity might
be strong enough to induce even so much as a 1% error?


Its about .001%. Thats significant enough that a tidal correction must
be made for prspecting by the gravity method.
You'd see more change in your weight by weighing yourself in Kenya compared
to Norway (several ounces) or at the bottom or top of Mt Everest (fraction
of ounce).
 




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