# Gravity transition directly at the underside of a "shell planet"

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• mgkii
In summary, the lecture discussed the basic divergence equations related to acceleration, mass density, and Newton's gravitational constant. It was shown that in a uniformly dense planet, the effect of mass "above you" cancels out. If the mass of a planet was concentrated in a shell, there would be zero gravity inside the shell. However, in a realistic case, the gravitational pull would continuously decrease as you descend through the shell. This was clarified in the more technical language of relativity.
mgkii
TL;DR Summary
Does gravitational pull transition immediately from g to zero underneath the shell of a "shell planet"
I'm watching the Stanford University Lecture series: Einsten's General Theory of Relativity presented by Leonard Susskind (who incidentally has to be one of the greatest educators I've ever watched).

Whilst deriving the basic divergence equations relating acceleration, mass density, and Newton's gravitational constant, he took a small diversion to show that Gauss' Therum shows you that if you place a test-mass inside a uniformly dense planet, then "little g" is only proportional to the mass inside the radius of the sphere you place the test mass on - i.e. the effect of all of the mass "above you" cancels out. So far so good!

He then went on to extrapolate that if the mass of a planet was concentrated entirely in a shell, then something inside the shell would effectively feel no gravity. However there was some debate with the class and the example ended in rather a lot of confusion!

Sorry for the long preamble - finally to my question! Did I take the correct understanding that someone standing on the surface of a "shell earth" (where all the mass of the Earth was concentrated in an arbitrarily thin shell at the surface) would feel the full 9.8m/s/s acceleration of Earth's gravity, but if you dug through that shell then you would transition immediately to a zero m/s/s gravity? This seems to be only outcome based on what I think I've understood, but it seems so alien I need to check my logical compass!

Thanks
Matt

PS - This is only Lecture 2 of 12... please go easy on me :-)

mgkii said:
Does gravitational pull transition immediately from g to zero underneath the shell of a "shell planet"

Only in the idealized case of a shell with zero thickness, which is not physically realistic.

In a realistic case of a shell with finite thickness, the "gravitational pull" continuously decreases from g to zero as you descend through the shell. Once you are inside the shell, yes, there would be zero gravity.

In the more usual technical language of relativity, the metric would continuously change as you descend through the shell, from the (curved) Schwarzschild metric for a mass ##M## (the total mass of the shell) outside to the (flat) Minkowski metric inside.

vanhees71
Thank you. That makes complete sense now. Happy for this thread to be closed!

## 1. How does the gravity transition work at the underside of a shell planet?

At the underside of a shell planet, the gravity transition is similar to that of a regular planet. The gravitational force is strongest at the center of the planet and decreases as you move towards the surface. However, at the underside of the shell planet, the gravitational force decreases as you move away from the center towards the outer edge of the shell. This creates a unique gravity transition where the force is strongest at the center and weakest at the outer edge of the shell.

## 2. What causes the gravity transition at the underside of a shell planet?

The gravity transition at the underside of a shell planet is caused by the distribution of mass within the shell. Since the mass is concentrated at the center of the shell, the gravitational force is strongest at the center and decreases as you move towards the outer edge of the shell.

## 3. How does the gravity transition affect objects on the surface of a shell planet?

The gravity transition at the underside of a shell planet can affect objects on the surface in different ways. For example, if an object is placed at the center of the planet, it will experience the strongest gravitational force and will be pulled towards the center. However, if the object is placed closer to the outer edge of the shell, it will experience a weaker gravitational force and may even be pulled towards the outer edge.

## 4. Can the gravity transition at the underside of a shell planet be measured?

Yes, the gravity transition at the underside of a shell planet can be measured using various methods such as gravitational mapping or measuring the acceleration of objects at different points on the surface. These measurements can help scientists understand the distribution of mass within the shell and how it affects the gravity transition.

## 5. Are there any other factors that can affect the gravity transition at the underside of a shell planet?

Yes, the gravity transition at the underside of a shell planet can also be affected by the rotation of the planet and the presence of other nearby celestial bodies. These factors can alter the distribution of mass within the shell and therefore, affect the gravity transition. Additionally, the composition and density of the shell can also play a role in the gravity transition.

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