00:01
For this problem on the topic of electromagnetic waves, we are told that beteljuice is a star that has a power output that is 10 ,000 times that of the sun, and we want to find the radiation pressure at a distance that is equal to that of uranus's orbit from the star.
00:17
Now, we'll use the fact that radiation pressure scales with intensity, and intensity goes linearly with the intrinsic power of the star, and inversely has the square of the distance away.
00:25
So if it is known that at the earth's orbit, the intensity due to the radiation at earth's orbit is 1 .35 kilowatts per square meter, this intensity can be related to the radiation pressure at earth's orbit and then to the hypothetical distance of uranus's orbit away from beetlejuice.
00:49
Note that the radius of the earth's orbit, re, is equal to approximately 1 .5.
00:59
Times 10 to the 11 meters, which is 1au.
01:04
And uranus's orbit, ru, is 2 .88 times 10 to the 12 meters, which is approximately 19 .2 au.
01:23
Now we have the radiation pressure at earth's orbit is proportional to the power of the sun over earth's orbit squared and the radiation pressure beetle juice is proportional to the power of beetle juice divided by its orbit ru squared and so we have r equals pru over p -r -e which is p -b -r -e squared divided by psru squared.
02:28
And so we can write this as the power of beetleju divided by the power of the sun times the radius of earth or the orbit of earth divided by the orbit of uranus squared.
02:45
And so we know the ratio of the powers is 10 to the power of 4 and the ratio of the orbits is 1 over 19 .2 and that's squared.
02:58
And so this value is equal to 27 .1...