Science answers why your weight varies depending on your location on earth and why the pendulum clock is slower at the equator

Somewhere in my last article I made mention of the different weight a 100lb individual will weigh in different planets. The "anomaly" was because of the different mass of those planets which affects the gravitational effect/pull on the person.

However, does it mean you can only feel this change in weight effect if you travel hundreds and even millions of kilometres?

Will it come as a surprise if a person from New Jersey USA weighs less, by some fraction, in Nepal without undergoing any weight loss program?

Let's jump right in and find out together.

For as long as I can imagine, the image on the right is my idea of the shape of the Earth, especially during my primary and high school science classes. It was later I got to know the actual shape of the Earth is nothing perfect like the picture on the right. It is something that is an oblate spheroid, and some people describe it as "pear" shape. If you click on the 3D animation on the left, you may get to see a shape that looks like a pear. The shape was as a result of the centrifugal force due to the spinning of the Earth.

The imaginary line that divides the earth at the centre bulges out like the pot belly of a man who likes beer a little too much. The centre is known as the Equatorial line.
Contrary to most bulges found in man, the Earth is a hard worker. The equator rotates at an incredible speed of up to 1000 miles per hour or 1600 kilometres per hour. This is almost twice the speed of a jumbo jet.

We should be feeling dizzy if it turns that much, wouldn't we? Thankfully, no. That would have been a problem, but physics have an explanation for that, anything that is moving at constant speed (no matter the rate) will not be felt. This is due to the tendency of a body to continue in its present state of motion unless acted upon by an external force. The law of inertia at play. The earth's rotation will not be felt unless, of course, it suddenly stops spinning, which we hope won't happen any time soon. The effect is similar to you enjoying that cold bottle of your favourite soda in a vehicle moving at a constant speed of 100km/hr. The liquid inside the cup will remain calm until a madman cuts off the driver and he suddenly applies the brake, making the soda spill all over your expensive designer suit. Bummer.

Happily, for some of us staying close to the equator, we will not experience the more spin effect except in things like the faster pendulum clock which spooked the 17th Century French astronomer. The explorer, Jean Richer, realised that his clock runs 2.5 minutes late

If we take a look at the period (T) of oscillation of a pendulum clock is a function of acceleration due to gravity in the area (g)

T≃2 π√(L/g)

where the L= length of the pendulum.

If a location has more gravity pull (g), the period will be shorter. A shorter period means the pendulum will swing faster.

Jean Richer, observed that the pendulum clock was slower by 2 1⁄2 minutes in Cayenne when compared to the time at Paris.

This phenomenon was because French-Guyana, the east coast of Soth American is nearer the equator compared to Paris. This fact makes the gravitational force not to be the same. Jean Richer inadvertently became the first person to notice that gravity is not the same at all locations on Earth due to the oblate shape of it.

Later, scientists were able to confirm the value of gravitational accerlaeration in Paris to be approximately 9.811 m/s², while that of Cayene is approximately 9.781 m/s²

The favourite gravitational constant magnitude value of 9.81m/s² is an average one taken to make high school physics classes easier.

Time goes a little bit slower at the equator than at the poles. The time is not the only thing affected; people also weigh less at the equator than at areas far from it, e.g. the Poles.

The equator may not be the only factor responsible for the different weight, however small, across the Earth's surface. Such place with very low gravity is Hudson Bay located in the northeastern part of Canada. The difference in gravity, though small (0.0005%), makes a significant difference.

The anomaly was a result of the recovering rocks in the area that was compressed by ice (during the ice age) which ended some 20,000 years ago. The melting ice creates convection current under the earth's mantle which in turn pulls off more of the Earth's mass on that location thereby reducing the gravity in the location. People over there will weigh less than their compatriots elsewhere.

REFERENCES

• ^Pendulum
• ^{World pendulum - A distributed remotely controlled laboratory (RCL) to measure the Earth's gravitational acceleration depending on geographical latitude}
• ^Gravity
• ^{Satellites solve mystery of low gravity over Canada}

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