Ok, so the intensity of light from a central source varies inversely as the square of the distance. So if you lived on a planet only half as far from the sun as our earth, then how would the light intensity on that planet compare with that on earth? And how would it compare to a planet ten times farther away than the earth?
2006-09-06 16:17:52 · 6 answers · asked by MegN 1 in Science & Mathematics ➔ Physics
The closer planet would receive 4 times as much light per square meter.
The farther planet would receive 100 times less light per square meter.
2006-09-06 16:24:47 · answer #1 · answered by Will 6 · 1⤊ 0⤋
Think of the light emitted by the sun at one instant as being on the surface of an expanding sphere of radius r. The surface area of a sphere is 4*pi*r^2. When this sphere is twice as big (2r) we get
a surface area of 4*pi*(2*r)^2 or 16*pi*r^2.
Dividing the first area by the second gives you 4. This means the area is 4 times as much. Since the the light is spread out 4 times as much the intensity is 1/4 as much.
Using the same formula with 10 times the radius, 10*r gives
4*pi*(10*r)^2 or 400*pi*r^2.
this is 100 times as much as the original area so the intensity is 1/100 th as much
2006-09-06 16:37:11 · answer #2 · answered by Demiurge42 7 · 0⤊ 0⤋
4 and .01(one hundreth), respectively.
If Intensity i ~ 1/re^2. (re = earth's radius.) Therefore,
If you have r = .5re:
i = 1/(.5re)^2 = 1/.25*1/re^2 = 4*i(at earth)
If you have r = 10re:
i = 1/(10re)^2 = 1/100*1/re^2 = .01*i(at earth)
Likewise, the planet at half earth's orbit recieves a luminar intensity 400 times that the planet at ten times earth's orbit.
2006-09-06 16:26:26 · answer #3 · answered by Rachel S 2 · 0⤊ 0⤋
Do you understand what is meant bysquare of the distance---half as far-or twice(factor of two) as close(means it would be brighter/more intense)--2x2=4 times as bright as on earth
ten times farther away(factor of ten)--not as bright---10x10=100 times dimmer than on earth.
2006-09-06 16:56:44 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Four times as bright as on earth. One one-hundredth as bright as on earth. The latter is why thermoelectric generators are used on spacecraft headed for the outer planets -- there is not enough sunlight for solar panels to power the electronics.
2006-09-06 16:23:57 · answer #5 · answered by Anonymous · 0⤊ 0⤋
1. closer planet : 4 times more luminous 2. fartrer planet
1/100th
2006-09-06 16:43:13 · answer #6 · answered by Dinker 2 · 0⤊ 0⤋