# Tag Archives: hole through the middle of the earth

## Falling Faster

A recent paper by  Alexander Klotz of McGill University, Montreal, has stirred a bit of interest in the pop-science press.  The paper looks at the old question of the time taken to fall through a hole passing through the centre … Continue reading

Posted in Excel, Maths, Newton | | 4 Comments

## The hole through the middle of the Earth – filled with air

Three air molecules go into a hole,  Well, I say three; could have been four or five.  Could have been nine or ten, doesn’t matter. Could have been fifteen, twenty – fifty. Round it up. Hundred. Let’s go mad, eh … Continue reading

Posted in AlgLib, Differential Equations, Excel, Maths, Newton, UDFs, VBA | | 4 Comments

## The hole through the middle of the Earth – revised transit time

In the previous post in this series I produced a table of acceleration due to gravity against depth from surface, based on the four layers of the Earth (Crust, Mantle, Outer Core, Inner Core), assuming a constant density for each layer.  … Continue reading

Posted in Differential Equations, Excel, Newton, UDFs, VBA | | 3 Comments

## The hole through the middle of the Earth – acceleration

In my first go at modelling a ball falling through a hole through the middle of the Earth I assumed constant density, and hence the acceleration at any point was proportional to the distance from the centre.  That is of course … Continue reading

## Using the AlgLib ODE (Runge-Kutta) Solver with Excel

Or to be more correct, the AlgLib Cash-Karp Solver, Cash-Karp being a refinement of the Runge-Kutta method of solving ordinary differential equations. Solution of differential equations is an iterative process requiring the repeated application of the solver routine followed by evaluation of … Continue reading

Posted in AlgLib, Beam Bending, Differential Equations, Excel, Maths, Newton, UDFs, VBA | | 8 Comments