[thedoc (OP)]

Where on the Earth would you experience the strongest and weakest gravity?
Asked by Tay Sharpe


                                       

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[chapter podcast=3027 track=11.03.27/Naked_Scientists_Show_11.03.27_8147.mp3]  or Listen to the Answer[/chapter] or [download as MP3]

[thedoc (OP)]

We put this to Dominic Ford from the Department of Physics in Cambridge...
Dominic -   The principle of physics that you need to work out the gravitational field around the distribution of matter is Newton’s Law of Gravity.  What that says is that every piece of matter in the universe attracts every other piece of matter in the universe with a force that decreases with the distance between the two masses, but it increases with the mass of those objects.  So, when it comes to the whole Earth, you have to add up the forces from all of the little bits that make up the sphere of the Earth, to work out what the total net force is, and that's actually a mathematical problem that gave Newton quite a headache when he was formulating his Law of Gravity and it led him to pioneer a new mathematical technique that we call calculus to add up those little forces.
[img float=right]/forum/copies/RTEmagicC_Geoids_sm_01.jpg.jpg[/img]But even though the math itself is quite tricky, it’s fairly easy to see roughly what the answer must look like because if you imagine that you burrow down into the Earth, you've then got some of the Earth above your head, and the rest of it below your feet whereas the before, the whole Earth was pulling you in one direction downwards.  So when you burrow down into the Earth, the gravitational forces are cancelling out and that means there must be a weaker gravitational field down inside the Earth than there is on the surface.
Similarly, if you travel upwards into space or climb a high mountain, then the Earth is further away and that means its gravitational pull is weaker, and so, you will weigh less.
Diana -   Standing at the top of Mt. Everest might make you feel a little bit lighter and that's in more than one way, I think!  But what might make us feel a stronger pull?
Dominic -   There are variations in the gravitational field across the surface of the Earth and that's actually a way that people look at the geology and the rocks that the Earth is made of.  So, if you're looking for a particular kind of rock, you can look for variations in the strength of gravity that tell you that you've got denser rocks or less dense rocks, and that might tell you about the rock composition below your feet.
The Earth does bulge out at its equator, but in fact, the amount by which it bulges out is exactly the right amount to cancel out the centrifugal force from the Earth’s rotation.  So, in terms of the downward force that you feel, it’s the same all over in the surface of the Earth.
Diana -   Certain rocks give certain areas of the earth’s stronger gravitational pull and the bulge at the earth’s equator counteracts the centrifugal force of the earth’s rotation, sounds simple.  On Facebook, Steven Duncan said that you should place your bathroom scales on the roof rather than in the basement.  Shawn Hoskins said that the Naked Scientists ought to fund a field trip for listeners to travel the globe to find out!

[Geezer]

I'd think it is on the Earth's surface, probably close to the equator, or is closer to the poles?

[imatfaal]

Just a few weeks ago the European Space Agency released results from its satellite GOCE which answers this question -
link here

In general it seems that "Gravitational acceleration at Earth’s surface is about 9.8 m/s², varying from a minimum of 9.788 m/s² at the equator to a maximum of 9.838 m/s² at the poles." from the same site.  But there is a lot of regional variation - some of which we cannot explain. From the maps available on the above site I guess you are lightest in Southern India/Sri Lanka and heaviest in Indonesia/Papua New Guinea

[Womble]

For the weakest gravity on earth you'll want to stand on the top of everest (you'll be further from the centre of the earth there), and for the strongest you'd need to stand (water pressure not withstanding) at bottom of the Marianas Trench (where you'll be closer to the centre of the earth).

[alftheelf]

Theoretically gravity is strongest at the centre of the Earth due to the gravitational equation. However the strength of gravity is very different from the strength of the effect. For example if you were at the centre gravity would be accelerating you the fastest, how ever this would be in all directions, so the overall effect of gravity would be 0 m/s^-2. But the place you would weigh the most I would assume is where there's a balance between distance from the centre and furthest of negative gravity pushing you up.

[imatfaal]

Theoretically gravity is strongest at the centre of the Earth due to the gravitational equation. However the strength of gravity is very different from the strength of the effect. For example if you were at the centre gravity would be accelerating you the fastest, how ever this would be in all directions, so the overall effect of gravity would be 0 m/s^-2. But the place you would weigh the most I would assume is where there's a balance between distance from the centre and furthest of negative gravity pushing you up.

Alf - not sure you're right there.  Although gravity varies inversely with r^2 - which might indicate that it should increase as you go down - the amount of matter attracting you to the centre also goes down.  The shell theorem tells us that matter further from the centre of mass than we are will not have an effect so although the force increases proportional to the second power as r decreases - the amount of mass attracting decreases with the volume inside us proportional to the third power.  In all force will is proportional to r when inside the sphere - so as r decreases so does the force. 

[Geezer]

Alf - not sure you're right there.  Although gravity varies inversely with r^2 - which might indicate that it should increase as you go down - the amount of matter attracting you to the centre also goes down.  The shell theorem tells us that matter further from the centre of mass than we are will not have an effect so although the force increases proportional to the second power as r decreases - the amount of mass attracting decreases with the volume inside us proportional to the third power.  In all force will is proportional to r when inside the sphere - so as r decreases so does the force. 

That's why I suspect it is at its greatest on the surface of the Earth. As you descend towards the center, the amount of matter above you increases.

[turnipsock]

Its got be on the surface as all the mass is behind you. It could be added to if the sun and moon were behind you as well.

I guess this question has been covered by that blooming Dr Cox already.

[@quantumapple]

@NakedScientists The GOCE answer kinda finalises the debate to be fair, it's the most accurate gravity measurement data we have isn't it?

was twittered by @quantumapple

[yor_on]

Now MR Quantum apple, why introducing facts into a otherwise interesting  discussion?

And a Quantum apple?
Isn't that self contradictory?

Myself I will put 5 p on the surface

[Raza]

As gravity depends on Mass and Square of Distance between object and centre of earth, According to this formula: GMe/Re^2. So Earth is considered to be spherical in shape, so it's distance from centre increases from equator and decreases from poles, so according to g= GMe/Re^2, Gravity is inversely related with distance, so on poles distance decreases and Gravity increases.

[Rexel]

Excited for the show! can't wait for it to be posted

- Fan from Philippines

[AntLewis]

Bit late now for the QotW show, but the BBC have some nice digestible info from the Goce satellite up today:
newbielink:http://www.bbc.co.uk/news/science-environment-12911806 [nonactive]

[Sid Tracy]

According to KahnAcademy if you travel toward the center of the earth, the force of gravity would diminish.  The center of mass would move as you move toward the center of earth and gravitional pull at the center of earth would be less as you move toward the center.