Effect of latitude on weight

[jimi]

Gravity is weaker at lower latitudes for two reasons.
The first is that in a rotating non-inertial or accelerated reference frame, as is the case on the surface of the Earth, there appears a 'fictitious' centrifugal force acting in a direction perpendicular to the axis of rotation. The gravitational force on a body is partially offset by this centrifugal force, reducing its weight. This effect is smallest at the poles, where the gravitational force and the centrifugal force are orthogonal, and largest at the equator. This effect on its own would result in a range of values of g from 9.789 m·s−2 at the equator to 9.832 m·s−2 at the poles.

The second reason is that the Earth's equatorial bulge (itself also caused by centrifugal force), causes objects at the equator to be farther from the planet's centre than objects at the poles. Because the force due to gravitational attraction between two bodies (the Earth and the object being weighed) varies inversely with the square of the distance between them, objects at the equator experience a weaker gravitational pull than objects at the poles.

In combination, the equatorial bulge and the effects of centrifugal force mean that sea-level gravitational acceleration increases from about 9.780 m/s² at the equator to about 9.832 m/s² at the poles, so an object will weigh about 0.5% more at the poles than at the equator

That explains a lot!

 

[Sgeir]

Aye, but, Jimi, there's also the issue that gravity decreases with altitude, since greater altitude means greater distance from the Earth's centre. All other things being equal, an increase in altitude from sea level to the top of Mount Everest (8,850 metres) causes a weight decrease of about 0.28%. (An additional factor affecting apparent weight is the decrease in air density at altitude, which lessens an object's buoyancy.) It is a common misconception that astronauts in orbit are weightless because they have flown high enough to "escape" the Earth's gravity. In fact, at an altitude of 250 miles (roughly the height that the Space Shuttle flies) gravity is still nearly 90% as strong as at the Earth's surface, and weightlessness actually occurs because orbiting objects are in free-fall.

 

[jimi]

aye Fg=GMm/r2=mg explains that cos r increases with height thus new r2 minus old r2 becomes the denominator

 

[Twister_Ken]

"weightlessness actually occurs because orbiting objects are in free-fall"

Free fall. You sure? Have you seen NASA's budget?

 

[Sgeir]

Hadn't thought of that. Does that mean that Helmert's equation (gφ = 9.780327 + 0.0516323sin2(&#966 + 0.0002269sin4(&#966) is just rubbish then?

 

[fireball]

What you're really trying to tell us is that you've weighed yourself and realise you weigh rather a lot more around your middle than you previously estimated ... /forums/images/graemlins/tongue.gif
And the lack of weight effect on your head has caused your hair to float off ... so now your a fat'n'bauld git! /forums/images/graemlins/laugh.gif

 

[Deleted member 478]

Ooo-err, all a bit too much for me Jimi.

Now tell me, is the wait to cross different longitudes an effective method of passing time?

 

[jimi]

In these girth-conscious times, even weight itself has weight issues. The kilogram is getting lighter, scientists say, sowing potential confusion over a range of scientific endeavor.

The kilogram is defined by a platinum-iridium cylinder, cast in England in 1889. No one knows why it is shedding weight, at least in comparison with other reference weights, but the change has spurred an international search for a more stable definition.

"It's certainly not helpful to have a standard that keeps changing," says Peter Becker, a scientist at the Federal Standards Laboratory here, an institution of 1,500 scientists dedicated entirely to improving the ability to measure things precisely.

Even the apparent change of 50 micrograms in the kilogram — less than the weight of a grain of salt — is enough to distort careful scientific calculations.

Dr. Becker is leading a team of international researchers seeking to redefine the kilogram as a number of atoms of a selected element. Other scientists, including researchers at the National Institute of Standards and Technology in Washington, are developing a competing technology to define the kilogram using a complex mechanism known as the watt balance.

The final recommendation will be made by the International Committee on Weights and Measures, a body created by international treaty in 1875. The agency guards the international reference kilogram and keeps it in a heavily guarded safe in a château outside Paris. It is visited once a year, under heavy security, by the only three people to have keys to the safe. The weight change has been noted on the occasions it has been removed for measurement.

"It's part ceremony and part obligation," Dr. Richard Davis, head of the mass section at the research arm of the international committee.

"You'd have to amend the treaty if you didn't do it this way."

That ceremony has become a little sorrowful as the guest of honor appears to be, on a microscopic level at least, wasting away

 

[MarkGrubb]

I don't want to be perdantic, but I will be.

Quote: Gravity is weaker at lower latitudes for two reasons.

Gravity is only weaker for one reason, the distance from the center of mass. The first reason you give has no affect on the strength of gravity itself.

 

[pyrojames]

Hmm. It depends how you define "weight". If you take is as the force you exert on a floor/ground etc due to a combination of your mass and the sum of the accelerations to which you are subjected, then the balance of the accelerations in space is zero (gavity minus inertial) and you are in fact weightless. If your definition of weight is restricted to the force that is created by the acceleration due to gravity on your mass, then you will rarely be weightless.

 

[graham]

So I dont need to loose 2 stone then.I can just move to Ecuador? /forums/images/graemlins/wink.gif

 

[Salty John]

When you're being pedantic it's always better to spell pedantic correctly, I find.

 

[snowleopard]

Absolute hokum my dear chap. It only seems as though gravity increases as you approach the poles. In reality it is just that those further north are more dense.

 

[thefatlady]

In a previous existence, I developed a system for measuring the content of very large oil tanks by <u>mass</u> to an accuracy of 0.05% of reading (more accurate than had ever been done before).

Our way of describing this was to observe that the difference in gravity between Aberdeen and London is 0.05%, so that if a tanker could be weighed absolutely correctly in Aberdeen and then in London, the apparent loss of oil would be equivalent to the maximum error of our system.