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How to mathematically calculate a fall through the Earth

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Huge thanks to the Great Courses Plus for sponsoring this video. Click here to check out the free trial: http://ow.ly/gSm4302OFJw

Watch the full integration! Worth it even just for the Simple Harmonic Motion which drops out at the end. https://www.youtube.com/watch?v=uUkCI1M6h_8

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. https://www.youtube.com/watch?v=Y64IHy1MGRQ

Python code that I used is here: https://www.dropbox.com/s/vbwymdxjz47bsrs/Earth_fall.py?dl=0

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. https://www.youtube.com/watch?v=urQCmMiHKQk

CORRECTIONS:
- 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.

Discuss on reddit: https://www.reddit.com/r/mattparker

Music by Howard Carter
Design by Simon Wright
Apple wrangling by Lucie Green

MATT PARKER: Stand-up Mathematician
Website: http://standupmaths.com/
Maths book: http://makeanddo4D.com/
Nerdy maths toys: http://mathsgear.co.uk/