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OfflineVisionary Tools
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What's the weight of 1kg at the poles and equator?
    #23489117 - 07/29/16 12:05 PM (7 years, 5 months ago)

Edit: Kilogram is a unit of mass. So, where I have written a kilo, read "10 newtons"

I looked up in a few places but no one has any numbers, just "very small" "insignificant".

So, I know there's a slight bulge at the equator, so, if there were no rotation of the earth (and no celestial objects pulling with their gravity) then, in theroy, a kilogram weight would weigh more at the poles than the equator, as it is closer to the center of mass.

But, the earth does rotate.
https://www.google.co.uk/search?q=rotational+speed+of+earth&ie=utf-8&oe=utf-8&gws_rd=cr&ei=ZZmbV-uVF4eta7-Mq4AP
http://www.dailymail.co.uk/sciencetech/article-2546864/How-fast-YOU-spinning-Earths-axis.html


Right, so, is it centrifugal or centripedal force? One of those. The rotation is faster at the equator.

This is where I need help with the numbers. I know from experiments I've done with spinning buckets of water, I can spin a bucket of water over my head using just my arms and I'm making enough centrifugical force to hold it in place. There's an old fairground ride I love called the rotor, which is a giant bucket that spins around and all the people stick to the sides of the rotor's wall, it's centrifugal force is strong enough to counteract earth's gravity.

Based on the rotational speed, can someone figure out how much (ignoring things like the moon, sun, juptier, a stray meteor) a kilogram weight should weigh at the equator?


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Edited by Visionary Tools (07/29/16 12:06 PM)


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OfflineBrian Jones
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Re: What's the weight of 1kg at the poles and equator? [Re: Visionary Tools]
    #23489678 - 07/29/16 03:48 PM (7 years, 5 months ago)

I'm no science guy (except social science), but I'm thinking, OK you can ignore a stray meteor, but how should you, or why would you, ignore the moon, the sun and Jupiter.


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OfflineVisionary Tools
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Re: What's the weight of 1kg at the poles and equator? [Re: Brian Jones]
    #23489880 - 07/29/16 04:57 PM (7 years, 5 months ago)

I want to make the sum as simple as possible so I can look at it, and go "yeah, that makes sense." After that, you can start adding the gravitational pull of celestial objects.


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Offlinejasen
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Re: What's the weight of 1kg at the poles and equator? [Re: Visionary Tools]
    #23494415 - 07/31/16 02:20 AM (7 years, 5 months ago)

First, the Earth is not a perfect sphere, it is slightly oblate--radius width between sides of the equator is slightly more than radius "vertically" between poles. (and this makes the effect you're talking about slightly greater)

Second, centrifugal force is actually not a thing.  Or it's a misnomer.  The deal is, an object in motion wants to stay in motion, in a straight line.  It requires another force to make it turn in a circle--in this case some of the force of gravity (centripetal force) is being wasted making objects turn in a circle as opposed to being used exclusively to pull them down.  So yep, some of that downward force is lost, making objects on the equator slightly lighter than at the poles.  (since weight is completely a function of gravity to start with, if you lose some gravitational force, you lose weight)

Without attempting to get into hideous physics maths right now, gravitational acceleration at the poles is about 9.83m/sec2, and at the equator it is about 9.78m/sec2.  This works out to an object weighing about %0.05 less at the equator than at a pole.


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OfflineVisionary Tools
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Re: What's the weight of 1kg at the poles and equator? [Re: jasen]
    #23494588 - 07/31/16 05:13 AM (7 years, 5 months ago)

Thanks Jasen.

Now, has anyone measured a kilogram at the poles and the equator to find if there's half a gram discrepancy?
I really thought the rotational speed at the equator would have a greater effect than that. It made me question why are rocket launches not done at the equator, instead of Florida and Baikonur.


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OfflineKryptos
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Re: What's the weight of 1kg at the poles and equator? [Re: Visionary Tools]
    #23497761 - 08/01/16 07:33 AM (7 years, 5 months ago)

As for rockets, I'm guessing geopolitics and the fact that the equator is not within the borders of countries capable of space launches. I know for a fact that they use the rotational speed of the earth to help launch rockets, though I am not certain exactly how (maybe they tilt it slightly?) Florida in particular is used because of large amounts of surrounding water in which to abort without flattening a city.

According to wikipedia, the speed boost of launching a rocket in Florida is 406 m/s compared to the equator where it is 463 m/s. Both figures are almost entirely insignificant considering the escape velocity of the Earth at 11.2 km/s.


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