# Gravity at the centre of the Earth?

• Beaujolais
In summary, the gravity on Earth's surface is approximately 9.8m/s/s, but at the center of the Earth, there would be no net force of gravity due to the spherically symmetric distribution of mass. However, the gravity within the Earth increases until it reaches its peak at the boundary of the outer core, with an acceleration of 10.88 m/s^2.
Beaujolais
I know gravity on the surface of the Earth is 9.8m/s/s from

g=GM/d^2
(6.7x10^-11)(6x10^24) / (6.4x10^6)^2 =9.81

But if you go to the center of the Earth will there be no gravity?
As the mass at the center will be nothing and the distance will be nothing?

As you proceed inwards towards the center, the net force of gravity is solely provided by the INNER massive ball (with center at the Earth's center); that is the outer shell of mass contributes nothing to the net force of gravity (we may prove it cancels out).

Thus, indeed, at the center of the Earth, there won't be any net force of gravity "felt".

Beaujolais said:
But if you go to the center of the Earth will there be no gravity?
Correct. If you imagine a hollowed out space at the center of the earth, and if you further treat the Earth as a spherically symmetric distribution of mass, then the gravitational field within that hollowed out space will be zero.

Beaujolais said:
I know gravity on the surface of the Earth is 9.8m/s/s from

g=GM/d^2
(6.7x10^-11)(6x10^24) / (6.4x10^6)^2 =9.81

But if you go to the center of the Earth will there be no gravity?
As the mass at the center will be nothing and the distance will be nothing?

Assuming you could actually exist in the center of the Earth, you would essentially be surrounded by equal mass therefore, not pulled in anyone direction greater than another. In essence, you would be weightless.

When you calculate the gravity from somewhere inside a sphere you can as has already been stated ignore the mass that is at a higher elevation than the point where we are measuring from. That being said the gravity can be calculated by the formula g=4pG(pi)r/3 where p is the density and r is the radius from the center if the body is of uniform density. This is not quite the case with the Earth. The inner core and outer core are much denser than the mantle so the gravity of the Earth actually goes up until you reach the boundary of the outer core, from then on it declines steadily to zero at the center.

what (aprox) would be the value of the FoG at its peak?

MoonKnight said:
what (aprox) would be the value of the FoG at its peak?

Using values I found on the internet I calculated an acceleration of 10.88 m/s^2 at the mantle/outer core boundary.

awesome, thanks

## 1. What is the force of gravity at the center of the Earth?

The force of gravity at the center of the Earth is approximately zero. This is because the mass of the Earth surrounds you in all directions, resulting in a net gravitational force of zero.

## 2. Does gravity change at the center of the Earth?

No, gravity does not change at the center of the Earth. The gravitational force is dependent on the mass of the objects involved and the distance between them, so as long as these factors remain constant, the force of gravity will not change.

## 3. Is there a point at the center of the Earth where gravity is strongest?

No, there is no specific point at the center of the Earth where gravity is strongest. Gravity is a force that acts between all objects with mass, so it is present everywhere within the Earth's core.

## 4. How does gravity at the center of the Earth affect time?

Gravity at the center of the Earth, or at any point within the Earth, does not have a direct effect on time. However, it can indirectly affect time by causing gravitational time dilation, where time moves at a slower rate in areas with stronger gravity.

## 5. Is there a way to measure the force of gravity at the center of the Earth?

Currently, there is no way to directly measure the force of gravity at the center of the Earth. However, scientists can use mathematical models and data from seismic waves to estimate the density and composition of the Earth's core, which can give insight into the force of gravity at the center.

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