I read zak's articles, and, I don't think the gravitational effect of the Moon on objects on the Earth's surface, is much (I think the articles agree).
I think the tides occur because, the Moon is pulling on the entire ocean. When the Moon is overhead, the sea level increases slightly beneath it, and the tide, "goes out". When the Moon is on the other side of the Earth, the sea level goes back down, and the tide, "comes in".
When you do the calculation (below), for the Moon's pull on individual objects on the Earth's surface, you find how tiny it is.
-----------------------------------------------------------
Newton's equation of the gravitational force between two objects is,
F = G * M1 * M2 / R^2
where,
G *= the universal constant of gravitation
M1 = the mass of one object
M2 = the mass of the other object
R *= the distance from the center of the first object to the center of the second object
http://en.wikipedia.org/wiki/Newton%...al_gravitation
-----------------------------------------------------------
At the lunar perigee (when the moon is closest to the Earth), the Moon is 221460 miles from the Earth (center to center).
At the lunar apogee (when the moon is farthest from the Earth), the Moon is 252700 miles from the Earth (center to center).
The mass of the Moon, is approximately 1/81 times the mass of the Earth.
http://www.enchantedlearning.com/sub...stronomy/moon/
-----------------------------------------------------------
The radius of the Earth is approximately 4000 miles.
http://geography.about.com/od/learna...earthfacts.htm
-----------------------------------------------------------
Let,
Fye = the force on you due to the Earth's gravity
Fym = the force on you due to the Moon's gravity, when the Moon is at it's perigee, and is directly overhead
Me *= the mass of the Earth
Mm *= the mass of the moon
My *= the mass of you
Re *= the distance from the center of the Earth to the Earth's surface
Rm *= the distance from the center of the Moon to the Earth's surface, when the Moon is at its perigee, and is directly overhead
Let, "~=", mean, "is approximately equal to".
Then,
Fye = G * Me * My / Re^2 .
And,
Fym = G * Mm * My / Rm^2 .
Therefore,
Fye / Fym *= (Me / Mm) * (Rm / Re)^2 ,
Fye / Fym ~= 81 * ((221460 - 4000) / 4000)^2 ,
Fye / Fym ~= 239400 .
This means that the Moon's gravitational force on you (or on anything on the Earth's surface), even when the Moon is as close to you as it can get, is tiny.
It means that if you weighed 100 pounds when the Moon was exerting its maximum gravitational pull on you, then, if the Moon suddenly disappeared, you would weigh approximately,
100 + 100 / 239400 = 100.00042 pounds.
-----------------------------------------------------------
Bookmarks