Hacker Newsnew | past | comments | ask | show | jobs | submitlogin

I wonder how many wats of power we would be able to generate before earth slows down for i.e. 1 second longer day.


I'm taking figures from https://en.wikipedia.org/wiki/Rotational_energy

Moment of inertia of the Earth: I=8.04e37

Angular velocity, with sidereal rotation period of 23.93 hours: ω0=2π/(23.93 × 3600)

Angular velocity, with sidereal rotation period of 23.93 hours plus one second: ω1=2π/(23.93 × 3600 + 1)

Rotational energy difference: .5 × I × ω0 ** 2 - .5 × I × ω1 ** 2 ≈ 4.96e+24 J

For comparison, according to https://ourworldindata.org/energy-production-consumption the total amount of energy consumed on Earth in 2023 was 180E3 TWh i.e. 6.48e+20 J

Slowing down the Earth by one second would be equivalent to 7661 times this amount.


According to Wikipedia [1] we consume 9717 Mtoe or equivalently 408 TJ (per year, although it is not explictely stated, which I find annoying).

The earth moment of inertia is about I=8e37 kg m2 [2]

The energy extracted by a slowdown of angular speed from wa to wb would be 1/2 I(wa2-wb2).

Approx wa=2pi/86400 and wb=2pi/86401. Energy extracted: 4.9e24J=4.9e12TJ.

We would have energy for about 12 billion years.

If I double check with Kagi's assistant with Claude 3.7 (I'm in my phone and I could easily have made an error) it starts with my exact reasoning and figures but messes up final numbers (so close!!!) to give a total of 40 billion years, which nevertheless is the correct order of magnitude.

[1] https://en.m.wikipedia.org/wiki/World_energy_supply_and_cons...

[2] https://scienceworld.wolfram.com/physics/MomentofInertiaEart...


That's easy to work out but I can tell you not it's going to be more than we will ever use.


You have no idea, what amount of energy we will be able to use the long run.


220, 221, whatever it takes.


We have potentially millions or billions of years of history in front of us. If we find a way and a motive to have self-sustaining communities outside this planet, and considering our own history, it looks at least plausible that we will continue spreading, after dominating an entire planet against the brutal odds of natural selection, which we basically hacked with our consciousness to reach this state.

Keep in mind that energy is not electricity. When a rocket is burning huge amounts of fuel to reach orbit, that's energy we're using, a lot of it.


"640K ought to be enough for anybody"


Typical human response





Guidelines | FAQ | Lists | API | Security | Legal | Apply to YC | Contact

Search: