Math Is Fun Forum

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Formula for ratio of weights at different latitudes

As you know, the Earth is not a perfect sphere so a person’s weight varies from place on place on the surface of the globe. Assuming that the Earth is an ellipsoid (that is, the intersection of the Earth with a plane passing through the Poles is an ellipse) then the person’s weight depends only on which latitude he or she is on.

Suppose he/she weighs

at latitude

N or S. Then his/her weight

at latitude

N or S is given by the following formula, which I calculated today:

[align=center]

[/align]

where

is the ratio of the Equatorial radius of the Earth to the Polar radius of the Earth.

Notes:

(1)

.

(2)

and

are weights, not masses. The person’s mass does not vary with location on Earth.

(3) Because the left-hand side is a ratio, it does not matter which unit you use to measure weight. You can use newtons, pounds, stones, or even the unscientific kilos. The utility of the formula is that if you know your weight at a particular latitude on Earth, you can calculate your weight at any other latitude on Earth.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Formula for ratio of weights at different latitudes

hi Jane

my name is Stefy.It is nice to finally meet you!

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Formula for ratio of weights at different latitudes

Hi Stefy. Nice to meet you too!