Today I started working on a new one of my “100 Proofs that the Earth is a Globe“. It’s the first one I’ve started for some time, because I’ve been distracted at home a lot with my wife working from home and haven’t been able to sit down knowing that I could work uninterrupted for several hours at a time. But today I just knuckled down and got started despite that. Normally I’d finish an article the same day I start, but I’m only about half way through, so hopefully I’ll be able to finish and post it tomorrow.
I took a break at lunch time to go do another 5k run. My fastest time for the 5k last year was 29:06, and last week I managed 29:16, so today my goal was to break 29 minutes. Unfortunately I miscounted laps and after sprinting the last couple of hundred metres and bending over exhausted to catch my breath while I checked my time on my phone, I discovered that I’d only covered 4.6 km! I still had a lap to go! I had to put the disappointment aside immediately and get the legs working again and set off on another lap…
But I managed it! My time for the full 5k today was 28:05. While running the last few laps I felt pretty exhausted and again really had to push through it mentally to avoid stopping, but now a few hours later my legs definitely don’t feel nearly as tired as last week.
I boasted to my friends on our online chat. One asked me if I was running laps of a street route, but I said no, the streets here are much too hilly for me to run, so I do laps of the nearby sports oval. And then this conversation happened:
Friend: Actually your run is consistent with orbiting a very dense object at the centre of the oval. #100ProofsGoreHillOvalIsABlackHole
Me: hmm…. I could calculate the mass, given the radius and speed… Damn, now I have to do it.
And I did. Approximating the oval as a circle and using the equation for a circular orbit: v = √(GM/r) gives the mass M of an object needed to cause me to orbit it at speed v and radius r. My speed was 5000/(28×60+5) = 2.97 m/s. I ran 11 full laps, totalling 5.14 km, so the radius of the oval is approximately (5140 m)/(11 laps)/(2π) = 74.4 m. Plugging the numbers in gives M = 9.81×1012 kg. Which is basically 1013 kg to any sensible degree of accuracy.
According to Wikipedia, 1013 kg is almost exactly the mass of comet 67P/Churyumov–Gerasimenko. Which is a little large to fit inside the oval. But never fear, for it’s also roughly the mass of two teaspoonfuls of degenerate neutron matter, which one could easily fit into the middle of a sports oval. If that much degenerate neutron matter had been in the middle of the oval, I could have stayed in orbit about it by running in a straight line. Although I suspect my orbit would decay rapidly after 5 km of running…
Friend: I’m so happy I nerdsniped you into doing this.
And just to include a photo: for dinner tonight I made a vegetable quiche, stuffed with potato, cauliflower, pumpkin, broccolini, onion, cherry tomatoes, eggs, and cheese:
New content today: