XPost: alt.usage.english
From: peter@pmoylan.org

On 09/03/25 09:58, Phil wrote:
> On 08/03/2025 22:46, Bertietaylor wrote:

>>>> It's just as implausible as the suggestion (easily disproved)
>>>> that the pressure is zero at the centre of the earth.
>>>
>>> The pressure is most certainly zero at the centre of the stars
>>> and planets. Read a first year book on physics.
>>
>> Which will say that within an enclosed surface with mass the net
>> gravitational force or pressure is zero.

Read that first year book yourself. Did you find the words "or
pressure"? No, I didn't think so. You've tried to conclude something
about the pressure from the gravitational force. That doesn't work,
because they are different quantities.

Gravitational force, like all forces, is a vector quantity. It has a
magnitude and a direction. That makes it possible that a number of
nonzero vectors can sum to zero; and, indeed, that is what happens
inside a spherical shell.

Pressure is a scalar. If you add two pressures, you get a higher
pressure. There's no such thing as a negative pressure to cancel out the
first pressure.

Think of a cone, or similar shape, whose point is at the centre of the
earth. You can separate out a section with thickness dr, and write down
the force balance equation for that slab. (This, too, is first year
physics.) From that you get a differential equation for the pressure as
a function of radius. No matter what simplifications you make, you will
get the same conclusion: the deeper you go, the higher the pressure.
Which is something that ocean divers can confirm from their own experience.

At the centre of the earth, the gravitational force is zero but the
pressure is at a maximum.

> Presumably, by an analogous argument, the pressure at the centre of a
>  balloon is also zero?

Actually, the gravitational force at the centre of a balloon is zero, if
you count only the force due to the balloon itself. But of course, you
do have to count the attraction from the earth as well.

Either way, what you conclude about the gravitational force says nothing
about the pressure. They're different quantities.

--
Peter Moylan       peter@pmoylan.org    http://www.pmoylan.org
Newcastle, NSW

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