# How varies the value of g

How varies the value of "g"

How varies the value of "g" in the depth of the earth.
the value of "g" at sea level is 9.8m/s2 what will be the value upward and downward the centre of the earth.
I know that at the centre of the earth the value is zero.
thanks

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#### pervect

Staff Emeritus
The gravitational acceleration of gravity 'g' as a function of the distance from the center of the Earth follow's Hooke's law, *if* we assume the Earth is spherical and of uniform density.

The way to calculate the force is fairly straightforwards. In Newtonian gravity, the gravity anywhere inside a uniform spherical shell is zero. Thus one divides the Earth into two parts - a spherical shell surrounding the observer, and a sphere underneath the observer.

http://www.merlyn.demon.co.uk/gravity1.htm#GoSp

goes through the details if you want to see a full calculation.

#### Meir Achuz

Homework Helper
Gold Member
At height H, g(H)=g(R)R^2/(R+H)^2.

#### Andre

But the answer is much more curious. The gravitaty is about constant in the mantle because on one hand you loose the gravity with an higher radius, which decreases the gravity, but get closer to the dense core which tends to increase the gravity. The gravity is highest at the Core mantle boundary, where the latter effect is winning and then goes to zero approaching the center of the Earth.

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I want to know just give me simple answer that.
when we go towards the centre of the earth in the depth of earth is the value of g decreases or increases if it is howmuch it increases or decreases.
thanks

#### quasar987

Homework Helper
Gold Member
You can read it from the graph: from the surface to about 4000 km deep, it is almost constant at ~10 m/s². then from 4000 km to 3500, it increases up to about 10.5 m/s², and then it decreases almost linearly (uniformly) down to 0 m/s² at the core.

#### Dr.Brain

Textually,yhe value of 'g' changes with:

(i) With Height
(ii) With Depth
(iii) With the latitudinal angle
(iv) With angular velocity of earth

BJ

#### Spin_Network

How varies the value of "g" in the depth of the earth.
the value of "g" at sea level is 9.8m/s2 what will be the value upward and downward the centre of the earth.
I know that at the centre of the earth the value is zero.
thanks
In order to understand Gravity at locations we have no access to 'Earth's Core', one can perform Gravitational experiments in the opposite direction, and thus deduce from experiment the of "g" over certain distance's.

For example, this is my thought experiment devised from imagination!

Imagine you are a Porter at a Conference hotel, there is to be a conference held on the 5th floor, so you and a fellow 'Porter/ess' have to move a large Table from the 1st floor to the 5th floor..using the stairs not on a lift. You choose to hold the backend of the Table, as you both lift the tabel the weight is equal for you both, your workmate proceeds up the stairwell, you start to notice that the weight of the table increase's!..whilst your workmate announcesey the Table has got a lot lighter..this is easy!

Now as you progress up the stairs, you take a break and drop the table at the 'level-landings' between floors, when you lift the Table again, it weighs the same for both Porters, until you climb the stairs again. WHen you arrive at the 5th floor the Conference Manager has been informed that the 'Gravitational Workshop' seminar has been relocated to the 10,000th floor!

As you move upwards the Table will start to 'Weigh' Less, at a certain point, the first Porter will start to have difficulty in his ability to place his feet upon the stairs. The Porter at the backend of the Table will, at a certain point be holding the Table(which by now has the first Porter clinging on to the Table, with his feet dangling above his head) with ease, as Earths Gravitational influence wane's the higher up the Stairs you climb, the Table will be influenced AWAY from the Porter at the Backend, it would start to Float upwards, eventually taking Both Porters Spacewards.

This a slight slant of the Eternal Ladder, but interestingly, if one has a Stairs that are going 'Into-Gound', to the Earths Core, then the same effect occurs, but in reverse..ie the first Porter going down the stairwell will be taking most of the Weight, and eventually he would be saved from the 'Core-Density' Gravitational effects, which would be at the Location of LEAST-FORCE..which is the point of Freefall, WITHIN THE EARTHS CORE?

thanks all members.

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