1. Space dust The sun has mass M, and emits light with total...

1. Space dust The sun has mass M, and emits light with total power P. Small dust particles are attracted to the Sun gravitationally, but repelled via the radiation pressure. Assume the dust particles are roughly spherical, with mass density $\rho$. a) Find the largest radius R a particle can have and not be ejected from the solar system. b) Calculate the radius R from part (a) if $\rho$=0.8 g/cm$^3$.

Transcript

00:01 I mean, this question basically look at something like silverwind.

00:03 I'm not sure what it's called silver wind, but it's kind of like that.

00:06 So i just call it silver wind.

00:09 So what's happening is the foreign situation.

00:11 So imagine the sun, which is here, right? you have the sun.

00:15 And of course, you meet photons, right? so a lot of radiation comes out.

00:20 A lot of radiation comes out.

00:22 You know, radiation kind of momentum, right? so imagine you have kind of a sphere here of some radios.

00:29 So this sphere absorbs the, radiation completely.

00:32 So it absorbs every income importance.

00:37 And that gives, that way, give you, give it the force going, you know, going this way.

00:41 Right.

00:41 So the force is like to actually be not larger than the gravitational force between this object and the sun.

00:48 And therefore, this, this object will be just be pushed away, right? be blasted off the solar system.

00:56 You can work out that, actually.

00:58 How large is the force acting on this radiation force, it f arrow, right? so the f .r is basically given by the intensity, okay? the intensity of the sound, suppose you have, suppose you have, let's say, distance, we need to look at the distance, right? and suppose you have a distance, let's say, so distance, they say this is arrow, right? so you can work out the intensity by the output power.

01:32 I'm not going to do this.

01:32 So i assume that intensity, the intensity at this point is i, right? the i multiplied by the cross -section of this ball.

01:42 That's four pi.

01:44 No, not four -pies.

01:45 This is pi just pi times hour squared.

01:49 R is the radius of this ball, right? and this is total amount of energy you see it, right? and that total amount of energy, that to the amount of energy actually when you are multiplied by the speed of light.

02:06 And that basically gives you, that basically gives you the, oh sorry, i think, i think it's not like this...

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