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Passionflower

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**The Schwarzschild Metric - A Simple Case of How to Calculate!**

There is thread open at https://www.physicsforums.com/showthread.php?t=431407 about tidal effects but there may be too many question or the chunk asked is simply to large to handle. At any rate, perhaps it is better to have a very simple question answered first.

Assume we have the following case:

Mass: 0.5

Schwarzschild Radius: 1

Two test clocks FRONT and BACK (FRONT always has a lower R coordinate value than BACK)

Suppose the tests clocks start to free fall from infinity with a ruler distance of 1.

Let's assume that the clocks, by having little rockets or a super rigid cable (I know this can't be the case but we have to start somewhere if we want to make any calculations), at all times maintain a ruler distance of 1.

**If anyone wants to chance these initial conditions fine, please then come with an alternative, use coffee ground, penguins, whatever you like, the objective is that we can**.

__calculate something not what tidal forces do in general terms__Now let's consider the case when the FRONT clock reaches the Schwarzschild coordinate: R = 2.

Then we can calculate the Schwarzschild coordinate of the BACK clock by solving:

[tex]

\sqrt {x \left( x-1 \right) }-\sqrt {2}+\ln \left( {\frac {\sqrt {x}+

\sqrt {x-1}}{1+\sqrt {2}}} \right) =1

[/tex]

This results in x = 2.757600642

It is perfectly understandable we do not get 3 because the ruler distances between R and R+1 increase for smaller values of R (See this graph https://www.physicsforums.com/attachment.php?attachmentid=28480&d=1285288006 ).

Now we can compute the (inertial) accelerations for both R values using:

[tex]{m \over r^2} { 1 \over \sqrt{1- {r_0 \over r}}[/tex]

Which gives:

FRONT Clock: 0.1767766952

BACK Clock: 0.08235933775 (as opposed to 0.06804138176 at R= 3!)

Now apparently tidal forces can be expressed in terms of accelerations, so now how do we go from here? If we assume there is no cable or rockets the clocks should be father apart due to tidal accelerations, but how far exactly?

Let's stay with the example and the given initial numbers so we can have

**a numerical example**.

Who can fill me in, or perhaps correct me where I am going wrong.

*Edited: fixed a mistake in the Latex formula*

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