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How to mathematically calculate a fall through the Earth

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Channel: Stand-up Maths
Categories: Physics   |   Math   |   Science  
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Watch the full integration! Worth it even just for the Simple Harmonic Motion which drops out at the end.

Try the ISS challenge! Will you get there before the after the International Space Station orbits half-way around the planet? Even if you don’t try to work it out, you can have a guess at the outcome.

Python code that I used is here:

My values:

R = 6,371,000 m (radius of the Earth)
G = 6.674 × 10^-11 m^3 kg^-1 s^-2 (gravitational constant)
M = 5.972 × 10^24 kg (mass of Earth)

Yes, people have since pointed out a similar topic was covered in a Minute Physics video. They skip over the "constant stuff" and how the mathematics is derived, but it’s a great look at how the density changes within the Earth and how that impacts the travel time. Well worth checking out as well.

- I accidentally wrote "v" instead "s" on the board in "s = ut + ½at^2". First spotted by Joel Low.
- Around 9:30 I used a dot for both 1,000's and decimal point. The first should be a comma. Spotted by Mezgrman.
- I normally play pretty fast and loose with centripetal force vs centrifugal effect; I think arguing about the difference is not useful so I often use them as synonyms. In this case, as Wayne Ernst politely pointed out, I should have said "centripetal force" not "centrifugal force". And they're right.

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MATT PARKER: Stand-up Mathematician
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