What would happen on the earth if we placed a huge mirror (focusing all sunrays in one point on earth) in space? [closed]

Question

Nice question for a sunny (at least here in Holland) Thursday morning. What kind of disasters would appear on our planet if we placed a huge (say, one with ten times the earth's diameter), mirror on the shadow side of the earth in space (aligned with the sun) with the capability to focus all sun rays in one little area of earth? Can a city be wiped out?

Answer 1

Yes, but you can't focus it to a city size. A 120000km mirror could wipe out life on the whole Earth, because the whole Earth would be in focus.

With a smaller, cheaper mirror you can delete a city from the map.

Answer 2

These questions are easy to answer: the purpose of this answer is merely to show you how easy it is. Given the easy availability of sources of data ('what's the radius of the Earth' or 'what's the Stefan-Boltzmann constant' is a question you no longer need to remember the answer to) it is really easy to work this sort of stuff out with a calculator.

First of all we need a couple of numbers: the radius of Earth, $R\approx 6.4\times 10^6\,\mathrm{m}$, and the solar constant, which is the power crossing the Earth's orbit from the Sun, $S\approx 1.4\times 10^3\,\mathrm{W/m^2}$.

So let this mirror be circular and have a radius of $10R$: its area is $\pi\times (10R)^2 \approx 1.3\times 10^{16}\,\mathrm{m^2}$. It therefore intercepts about $1.8\times 10^{19}\,\mathrm{W}$.

Lets assume it focusses all this power on a circle or radius $r$, and therefore of area $\pi r^2$. The power per unit area -- the incoming flux of radiation -- is $1.8\times 10^{19}/(\pi r^2) \approx 5.7\times 10^{18}/r^2\,\mathrm{W/m^2}$.

So, consider a city a hundred miles in radius: the incoming flux is about $F\approx 2.2\times 10^8\,\mathrm{W/m^2}$.

We can then do a naive calculation to work out the temperature (this calculation has a dangerous problem: see below): assume the city is a black body, then its temperature $T$ is given by

$$T = \left(\frac{F}{\sigma}\right)^{1/4} \approx 7900\,\mathrm{K}$$

If this calculation were correct, then it is clear that everyone would die. However the calculation is not correct, because such a mirror can never raise the temperature above the temperature of the thing whose light it is focussing, which in this case is the surface of the Sun, which is about $5800\,\mathrm{K}$. This is due to something called 'conservation of etendue' which has been discussed in answers here: essentially the mirror can't focus on a spot this small which prevents you getting above the temperature of the source.

However the calculation is right enough: such a mirror would happily raise the temperature of small countries to thousands of degrees. Indeed such a mirror would happily raise the temperature of the whole planet to a point where life was not possible: the Earth's surface area is about $5.1\times 10^{14}\,\mathrm{m^2}$ and just plugging this into the black-body formula we get a temperature of a little short of 900K: well above boiling!

Answer 3

What a destructive thought. :)

This will focus the sun light from evry possible corner on the focal point of the parabolic mirror.

Since normally, in outer space temperature goes beyond 120°C when the sun light is scattered over the space.

And when all its rays will be focused, it may go beyond 1000°C.

Now to your question, leave the city Earth would be a goner. Even if it do not destroy earth or melt it, It would be enough to disturb the physical phenomenons all over the Earth like temperature, water will evaporate and other air current etc. required to sustain life. Due to disturbance in air currents tornadoes at various place may occur.

And i think due to energy from sunrays even the gases in our atmosphere may escape.

So Not only the city but whole Earth will and no one will live to see much. This would be like human extinction.

Note: We need to consider that the mirror size and plane do not vary with the temperature variation in space. Also mirror should be able to withstand the temperature received from sun.

Answer 4

The first thing that would happen is that it would get extremely hot, as heat usually accompanies light, then all water around that area would evaporate, killing plants and some animals, then the area would likely become a dessert. If enough light was focused then theoretically you should be able to wipe out a city, but by then you would most likely have wiped out life on the rest of the planet by melting the ice caps and supper heating the rest of the planet because the ozone layer reflected most of the heat back down onto the planet which would turn most of the light to heat, if the ozone layer is still there, or most people would receive extreme cases of cancer and die, due to a missing ozone, and if it gets hotter still you could probably melt the planet.
And that is only if you you can get enough light onto the mirrors reflective surface, build a big enough mirror, and make it the correct shape and angle to focus it on a single point.
So in short if you could do it you would probably cause floods, droughts, mass destruction/death,and probably destruction of the Earth, not just a city.

Answer 5

I recently took a lense with a diameter over a meter long and focused the sun light onto a piece of metal (pop can) which promptly began to vaporize. The earth has a diameter on the order of tens of millions of meters, and you say you want a lense with a diameter ten times that... so you'd be collecting more light than hundreds of millions of what would be necessary to destroy a pop can. Yes you could destroy a city with such a beam. However the materials required to construct such a device would certainly be enough to stop the project.