4 ms·
Forgive me, for I am doing an end-run around a HN rule (replying to a reply to a reply). But it seems an entertaining question... > What if you radiated a Sun'
by mgsouth 4y ago
Forgive me, for I am doing an end-run around a HN rule (replying to a reply to a reply). But it seems an entertaining question...
> What if you radiated a Sun's worth of energy (10^26 Watts) out of 1 square meter?
* Blackbody temperature: 2 x 10^8 K.
Peak blackbody wavelength: Wolfram didn't like that question. However, it did helpfully note that it was twice the temperature needed for controlled nuclear fusion, and 5e7 K above the temperature at which the triple alpha process occurs inside stars.
It also noted that it was equivalent to 17 keV. This would, suprisingly to me, be X-rays and not gamma; the cut-off is 100 keV. 17 keV is a photon wavelength of 73 picometers (7.3e-11 m); a helium atom's diameter is about 62 pm.
* Luminosity would be about 4e15 lux. It would, of course, be twice as bright as the sun (equivalent to seeing both solar hemispeheres at the same time.) You would be able to see the Earth from lightyears away.
* Radiation pressure would be 730 x 10^12 newtons (80 gigatons).
* This would accelerate the Earth by 1.2e-10 m/s^2. Even if sited at one of the poles, that's only 4 millimeters/sec over one year. Not useful for jaunting around the Solar System except on geologic timescales.
* Asteroid Apophis is a whole 'nother matter. It's estimated to be 6 x 10^10 kg. Assuming we left its destruction to THE VERY LAST SECOND (i.e., distance 0), the radiation pressure would accelerate it at 36 km/s^2. (Yep. You try it: [0]; it's x 2 because it is reflecting) Of course, it would melt it in about half a nanosecond (literaly).
* Mars' moon Phobos would fare better. Assuming the radiator is a 73 picometer X-ray laser with 1.1 m diameter (1 m^2 area), beam divergence (based on no-doubt-poorly-applicable-in-reality formulas) would be about 2e-11 radians. At conjunction, the Earth and Mars are a maximum of 400 million km apart. Wolfram thinks (it ain't easy calculating the sine of 2e-11) the beam would diverge to about 8 meters wide at that distance. Phobos masses about 1e16 kg. It would only accelerate at 0.14 m/s^2, or 12 km/s/day. And it wouldn't melt for at least 80 milliseconds.
[0] https://www.wolframalpha.com/input?i=730e12+newtons+*+2+%2F+4e10+kg https://www.wolframalpha.com/input?i=730e12+newtons+*+2+%2F+...
- taneq 4y agosin(2e-11) is almost exactly 2e-11 since sin(x) ~= x for small x. :)