How far away can you feel something hot?

[corrado33]

Was faced with an interesting question the other day.

Say I have a 1000 C object with no insulation in air. How close would my hand have to be to it to feel a temperature change. (Assuming a human hand can distinguish +- 1 C.)

What equations would one use to calculate that?

[helius]

The Stefan-Boltzmann equation and the inverse-square law would do it.
See also https://en.wikipedia.org/wiki/Radiance

[Vipitis]

I think the sun is really far away, and I can definitely feel it's heat

[WastelandTek]

I think the sun is really far away, and I can definitely feel it's heat

beat me to it

[hamster_nz]

It must be proportional to apparent size (their must be a more correct term for this).

If the 1000C object is as big disc, as thin as paper, then side on it will have minimal heating, however front on it will be very hot indeed.

Reminds me of a 'proof' the the universe and stars are not unchanging and infinite. It it was, then everywhere you look in the sky would be looking directly at a star, and each would be as hot as the sun. Hence the dome of the sky would be as bright as the sun, so surface of the earth would be this temperature too.

[bap2703]

It must be proportional to apparent size (their must be a more correct term for this).

If the 1000C object is as big disc, as thin as paper, then side on it will have minimal heating, however front on it will be very hot indeed.

This apparent size is called the "solid angle" (it's just an angle but in 3D).

[grumpydoc]

I think the sun is really far away, and I can definitely feel it's heat

beat me to it

Me three

I've often thought that it is pretty impressive to be stood 150 million kilometres from something and to still feel warm

The total solar output is slightly mind blowing - the average distance to the sun is 149597870700m, the surface area of a sphere of that radius is 2.8123x10²³m². I think that the figure of average insolation 1362W/m² at the top of the atmosphere given by Wikipedia is at the equator so that is 1361x2.8123x10²³m² or 3.83x10²⁶W.

To put it another way that is (if I have it right) approx 383 trillion TW over the whole solar surface in the visible and IR spectrum.

No wonder it feels a bit warm.

[jwm_]

Its crazy how much energy is all locked up sitting around being  matter in stars. My favorite order of magnitude space fact is that a supernova 100 million miles away  will be brighter than a nuclear bomb pressed against your eyeball. By 9 orders of magnitude. https://what-if.xkcd.com/73/

[StillTrying]

Just to be awkward, I've always thought that the detection of heat or cold should be considered a separate sense from touch.

[komet]

Just to be awkward, I've always thought that the detection of heat or cold should be considered a separate sense from touch.

It is. The "sense of touch" is a concept taught in primary school and not used afterwards.