Earth/Moon Gravity

Richard Heathfield wrote:
said:

I'm told the mass of the moon is about 1/80 th (one eighty-th) of the
Earth's. Is there some simple calculation that can show the ratio of
the earth's gravity to the moon's? (which I'm told is about 6:1)

thanks for any ideas. Stan


Given the relative masses of the Earth and Moon, and their relative radii,
yes there is.

If we don't mess with our units, then we can see that a = M / d * d

Taking your (slightly inaccurate) 1/80th figure for the mass of the Moon
relative to the Earth, it has a mass in "Earth mass units" of 1/80 or
0.0125. The radius of the Moon is around 0.27 times that of an Earth
radius. So the acceleration due to the Moon's gravity is
0.0125 / (0.27 * 0.27). Now, 0.27 squared is 0.0729, so the Moon's
acceleration due to gravity is around 0.0125 / 0.0729 = 0.17ish, or around
1/6 of Earth's gravity.



A related question:

what minimal set of knowledge and technology is needed to determine
the size and the mass of the moon (either in explicit units (km, kg)
or in earth units (R_e, M_e))?

what minimal set of knowledge and technology is needed to determine
the size and the mass of the moon (either in explicit units (km, kg)
or in earth units (R_e, M_e))?

Wikipedia...

HTH

--
Kev

In article . com,
sasha semenov wrote:

A related question:

what minimal set of knowledge and technology is needed to determine
the size and the mass of the moon (either in explicit units (km, kg)
or in earth units (R_e, M_e))?

Well, the Greeks knew the distance from the Earth to the moon and
thus the size of the moon. If you assume the moon has the same
density as the Earth then you can get the mass as a percentage
of the Earth's mass. Add Newton's Law of Universal Gravitation,
make a hand-waving guess as to the Earth's density, and you can
get the absolute mass of both (or you can go the route of measuring
the gravitational constant directly, but that's too much like real
work).

Alan
--
Defendit numerus

In article ,
Kevin Stone wrote:
what minimal set of knowledge and technology is needed to determine
the size and the mass of the moon (either in explicit units (km, kg)
or in earth units (R_e, M_e))?

Wikipedia...

I'm pretty sure Wikipedia isn't necessary; it's a fairly recent
phenomenon. The ancient greeks were able to discover the radius of
the earth; all that's needed there is geometry and measurements taken
at the right time. They also had the earth-moon ratio, which was done
using eclipses and geometry.

Masses are much harder; I think you need Newton for them, applied to
data obtained by observing the perturbation of the Earth's orbit
caused by the moon.
--
There's no such thing as a free lunch, but certain accounting practices can
result in a fully-depreciated one.

what minimal set of knowledge and technology is needed to determine
the size and the mass of the moon (either in explicit units (km, kg)
or in earth units (R_e, M_e))?

Wikipedia...

I'm pretty sure Wikipedia isn't necessary; it's a fairly recent
phenomenon. The ancient greeks were able to discover the radius of
the earth; all that's needed there is geometry and measurements taken
at the right time. They also had the earth-moon ratio, which was done
using eclipses and geometry.

I'll race you...

--
Kev

"Alan Morgan" wrote in message
...
In article . com,
sasha semenov wrote:

A related question:

what minimal set of knowledge and technology is needed to determine
the size and the mass of the moon (either in explicit units (km, kg)
or in earth units (R_e, M_e))?

Well, the Greeks knew the distance from the Earth to the moon and
thus the size of the moon. If you assume the moon has the same
density as the Earth

Quite a big assumption - you're really comparing chalk and cheese here!

then you can get the mass as a percentage
of the Earth's mass. Add Newton's Law of Universal Gravitation,
make a hand-waving guess as to the Earth's density, and you can
get the absolute mass of both (or you can go the route of measuring
the gravitational constant directly, but that's too much like real
work).

Alan
--
Defendit numerus

In article ,
Mike Terry wrote:
"Alan Morgan" wrote in message
...
In article . com,
sasha semenov wrote:

A related question:

what minimal set of knowledge and technology is needed to determine
the size and the mass of the moon (either in explicit units (km, kg)
or in earth units (R_e, M_e))?

Well, the Greeks knew the distance from the Earth to the moon and
thus the size of the moon. If you assume the moon has the same
density as the Earth

Quite a big assumption - you're really comparing chalk and cheese here!

Oh, come on. I'm only off by 50%. I'm not sure how you could compute the
mass of the moon without making that assumption (still assuming minimal
knowledge and technology here).

Alan
--
Defendit numerus

Alan Morgan said:

In article ,
Mike Terry wrote:
"Alan Morgan" wrote in message
...
In article . com,
sasha semenov wrote:

A related question:

what minimal set of knowledge and technology is needed to determine
the size and the mass of the moon (either in explicit units (km, kg)
or in earth units (R_e, M_e))?

Well, the Greeks knew the distance from the Earth to the moon and
thus the size of the moon. If you assume the moon has the same
density as the Earth

Quite a big assumption - you're really comparing chalk and cheese here!


Oh, come on. I'm only off by 50%. I'm not sure how you could compute the
mass of the moon without making that assumption (still assuming minimal
knowledge and technology here).

The mass of the Moon relative to the Earth was certainly known in the late
18th Century and probably long before. In 1798, the (absolute) mass of the
Earth was calculated (Cavendish got to within 1% of the true value - not
bad for 208 years ago), and the Moon's mass was directly calculable as a
consequence.

--
Richard Heathfield
"Usenet is a strange place" - dmr 29/7/1999
http://www.cpax.org.uk
email: rjh at the above domain, - www.

"Alan Morgan" wrote in message
...
In article ,
Mike Terry wrote:
"Alan Morgan" wrote in message
...
In article . com,
sasha semenov wrote:

A related question:

what minimal set of knowledge and technology is needed to determine
the size and the mass of the moon (either in explicit units (km, kg)
or in earth units (R_e, M_e))?

Well, the Greeks knew the distance from the Earth to the moon and
thus the size of the moon. If you assume the moon has the same
density as the Earth

Quite a big assumption - you're really comparing chalk and cheese here!


Oh, come on. I'm only off by 50%. I'm not sure how you could compute the
mass of the moon without making that assumption (still assuming minimal
knowledge and technology here).

Don't worry Alan - I was just making a little joke! You know it's alleged
by some that the moon is made of cheese? And in English we have the
expression "chalk and cheese" hence the smiley (well, I thought it was
amusing anyway. I didn't spot the sci.astro in the newsgroup list!)


Alan
--
Defendit numerus

This is one of my favourite puzzles -

You may assume knowledge of Newtonian physics, and of the general
structure of the solar system, but not of any of its dimensions. Using
only your own body as a measuring instrument, find which is denser, the
sun or the moon.

Nick
--
Nick Wedd