How to mathematically calculate a fall through the Earth

Watch the full integration! Worth it even just for the Simple Harmonic Motion which drops out at the end.    • Integrating a fall through the Earth   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.    • Race the ISS through the Earth   Python code that I used is here: https://www.dropbox.com/s/vbwymdxjz47... 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.    • How Long To Fall Through The Earth?   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:   / 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/