pendulums in strong G

[RichD]

You're on the surface of a large dense planet, with
G field strong enough that general relativity applies,
the weak field approximation fails.

Does a pendulum still act like a pendulum? i.e. swings
back and forth, useful as a clock?


--
Rich

[Richard Hertz]

You should read more about the history of developments in physics in the period 1750-1810, when the work
of Euler (F=m.dv/dt) spread along Europe and a new generation of polymaths (in particular at France) developed
the mathematics of newtonian mechanics and (Laplace) married it with celestial mechanics.

The equation of pendulum clocks reached perfection around 1790, and the simple formula of the period was
developed, providing that deviations from the vertical are lower than 15°. Pendulum clocks were calibrated at
different parts of Europe and Africa, to adjust the length of the swinging arm to 1 second period. The history
about these developments are easily available online, in French sites.

Equation of the pendulum:

T = 2π √L/g₀

T: Period
L: Length of pendulum
g₀: acceleration due to gravity

The results of this equation were known with 7 digits accuracy by the times of Von Soldner theory of light deflection (1801),
specifically for a given coordinate at France.

As the equivalence of inertial and gravitational masses were widely accepted by then (250 years and counting), the equation
could be formulated using Newton's Law with Gauss values for G (Cavendish value was accepted much later).

g₀ = G.Me/R₀²

so,

T = 2π √L/g₀ = 2πR₀ √L/(G.Me)

g₀ is the value of gravity at the designated place, on Earth (3D coordinate).

T = 2πR₀ √L/(G.Me)

If the radius increase, so does the period T. It forces L to be lower.
If planet mass increases, T decreases, so L has to increase to compensate.

The main idea behind the pendulum clock is that exactly half period gives exactly 1 second.

Relativity doesn't have a single saying here. Newton always prevails.

[J. J. Lodder]

RichD <r_dela...@yahoo.com> wrote:

> You're on the surface of a large dense planet, with
> G field strong enough that general relativity applies,
> the weak field approximation fails.

None such exist.
You would need a white dwarf, or a neutron star.

> Does a pendulum still act like a pendulum? i.e. swings
> back and forth, useful as a clock?

Yes, why not?
You would have a problem finding a rod
with the required tensional strenth though,

Jan

[J. J. Lodder]

Richard Hertz <hert...@gmail.com> wrote:

> On Wednesday, May 25, 2022 at 4:00:17 PM UTC-3, RichD wrote:
> > You're on the surface of a large dense planet, with
> > G field strong enough that general relativity applies,
> > the weak field approximation fails.
> >
> > Does a pendulum still act like a pendulum? i.e. swings
> > back and forth, useful as a clock?
> >
> >
> > --
> > Rich
>
> You should read more about the history of developments in physics in the
> period 1750-1810, when the work of Euler (F=m.dv/dt) spread along Europe
> and a new generation of polymaths (in particular at France) developed the
> mathematics of newtonian mechanics and (Laplace) married it with celestial
> mechanics.

Better yet, start in the 17th century.

> The equation of pendulum clocks reached perfection around 1790, and the
> simple formula of the period was developed, providing that deviations from
> the vertical are lower than 15°. Pendulum clocks were calibrated at
> different parts of Europe and Africa, to adjust the length of the swinging
> arm to 1 second period. The history about these developments are easily
> available online, in French sites.
>
> Equation of the pendulum:
>

> T = 2π √L/g?
>
> T: Period L: Length of pendulum g?: acceleration due to gravity

>
> The results of this equation were known with 7 digits accuracy by the
> times of Von Soldner theory of light deflection (1801), specifically for a
> given coordinate at France.

Ah, France, France and France.
(they are almost as good at it as Russians)
In reality Huygens knew all this a hundred years earlier.

The French too of course, because Huygens told them.
He was a founding member of the French Academie des Sciences, (1666)

Jan

[mitchr...@gmail.com]

On Thursday, May 26, 2022 at 1:23:21 PM UTC-7, J. J. Lodder wrote:
> Richard Hertz <hert...@gmail.com> wrote:
>
> > On Wednesday, May 25, 2022 at 4:00:17 PM UTC-3, RichD wrote:
> > > You're on the surface of a large dense planet, with
> > > G field strong enough that general relativity applies,
> > > the weak field approximation fails.
> > >
> > > Does a pendulum still act like a pendulum? i.e. swings
> > > back and forth, useful as a clock?
> > >

If it is the same pendulum it will be pushed faster...
We can test on the Moon. The same pendulum will swing
six times slower.

Pendulums don't swing weightless in space.
Why do they need weight to swing?
What pushes the pendulum? God is creating it.

[Richard Hertz]

Six times slower??

Did you even care to look at the equation and grasp its meaning?

Try again with the pendulum clock at the Moon. You'll be surprised with the result of the period T.

[mitchr...@gmail.com]

You have it backward rich. Your equation isn't objective.
More gravity means a faster push not slower.
Less gravity means lesser push.
You can't use something that has never happened.
There have been no pendulums on the Moon.

Mitchell Raemsch

[Richard Hertz]

The equation couldn't be simpler, and is exact for angles lower than 15". It has been so for 250 years.

The period T of the pendulum clock is proportional to the inverse square root of g.

If g is higher than 9.81 m/s2, then the period T is lower than 1 second. So, the clock ticks at a higher rate.

If g is lower than 9.81 m/s2m, then the inverse happens. T is higher than 1 second, and the clock ticks at a lower rate.

I don't see why this is so difficult to understand.