Hi manofwar!!
If the earth was not spinning, would a person weigh more?
The answer is yes on the Equator, where the centrifugal acceleration
due by the Earth rotation rise the maximum. But in the poles the
effects of the Earth´s rotation are null, so the weight without
rotation will be the same.
If so, by how much?
In the Equator the weight will be 0.3468% greater, and in the poles
will be the same.
To see how to obtain, aproximately, this data I you must visit the
following page: "Curious About Astronomy - Does your weight change
between the poles and the equator?"
http://curious.astro.cornell.edu/question.php?number=310
Does a person weigh more at the North Pole than at the equator where
centrifugal force is greater?
The answer is yes, the centrifugal force pull the person out of the
Earth and the gravity pull the person to the center of the Earth, then
weight is:
W = Fg - Fc where Fg is the gravity force and the Fc is the
centrifugal force.
In the North Pole Fc is null, then the weight is greater here.
Maybe the greater distance from the center of the earth at the equator
cancels the difference out?
Here you have a little confusion: The answer is NO, because if the
distance from the center of the Earth is greater, the weight will be
smaller:
G x M1 x M2
Fg = ------------------ (Newton's Law of Gravitation).
R^2
Then the person weigh more in the Pole because here he is closer to
the center of the Earth than in the Equator.
I addition we have the fact that the person weigh more in the North
Pole than in the Equator due the Earth rotation.
Then the weight difference considering the closer distance of the
North Pole to the center of the Earth is greater.
I found the exact values of related measures at the "MikaP Astro -
Earth" page:
http://www.ursa.fi/~mpi/earth/
From this page we have the following data of the Earth:
-Mass: 5.9763E27 g
-Mean equatorial radius: 6378.245 km (A.A.Izotov,1950);
6378.077 km (I.D.Zhongolovich,1956)
-Difference in equatorial and polar semi-axes:
21.382 km (A.A.Izotonov,1950)
21.500 km (I.D.Zhongolovich,1956)
-Mean radius: 6370.949 km
-Mean acceleration of gravity at equator:
9.780573 m/s^2 (I.D.Zhongolovich,1952)
-Mean acceleration of gravity at poles:
9.832251 m/s^2
-Mean acceleration of gravity for entire surface of terrestial :
9.797830 m/s^2
-Ratio of centrifugal force to force of gravity at equator:
0.0034677 (0.34677%)
And a lot more.
For more reference and nice info related you can read the following
articles:
"The Bulging Earth" from Math Pages:
http://www.mathpages.com/home/kmath182.htm
"Weight Changes with Position On/In Earth" by J. D. Jones from M.
Casco Associates:
http://mcasco.com/QA22.html
At "The Math Forum - Ask Dr. Math" you can read a very interesting
discussion about the "Effects of the Earth's rotation on objects" and
the nature of the centrifugal force. The discussion is entitled: "If
the Earth Stopped Rotating...":
http://mathforum.org/library/drmath/view/56342.html
Another article: "Gravity variation from the equator to the poles" by
Ramin Amirmardfar:
http://www.geocities.com/ramin1102000/chap2-2page.html
I answer this question based in my own knowledge and using the
following search strategy:
Search engine: Google
Keywords and results pages:
earth gravity centrifugal ratio
://www.google.com/search?q=earth+gravity+centrifugal+ratio&btnG=Google+Search&hl=en&lr=&ie=ISO-8859-1
weight poles centrifugal
://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&q=weight+poles+centrifugal&btnG=Google+Search
I hope this helps you, but if you need some clarification, please post
a request for it before rate my answer. |