Radiation Pressure As a comet swings around the Sun, ice on...

Radiation Pressure As a comet swings around the Sun, ice on the comet's surface vaporizes, releasing trapped dust particles and ions. The ions, because they are electrically charged, are forced by the electrically charged solar wind into a straight ion tail that points radially away from the Sun (Fig. 33-39). The (electrically neutral) dust particles are pushed radially outward from the Sun by the radiation force on them from sunlight. Assume that the dust particles are spherical, have density $3.5 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3},$ and are totally absorbing. (a) What radius must a particle have in order to follow a straight path, like path 2 in the figure? (b) If its radius is larger, does its path curve away from the Sun (like path 1) or toward the Sun (like path 3 ?

Radiation Pressure
As a comet swings around the Sun, ice on the comet's surface vaporizes, releasing trapped dust particles and ions. The ions, because they are electrically charged, are forced by the electrically charged solar wind into a straight ion tail that points radially away from the Sun (Fig. 33-39). The (electrically neutral) dust particles are pushed radially outward from the Sun by the radiation force on them from sunlight. Assume that the dust particles are spherical, have density $3.5 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3},$ and are totally absorbing. (a) What radius must a particle have in order to follow a straight path, like path 2 in the figure? (b) If its radius is larger, does its path curve away from the Sun (like path 1) or toward the Sun (like path 3 ?

Key Concepts

Size-Dependent Scaling of Forces

The effect of radiation pressure on a particle is highly dependent on its size. Since the force from radiation pressure is proportional to the cross-sectional area (which scales as the square of the radius) and the mass of the particle scales as the volume (which scales as the cube of the radius), smaller particles are proportionally affected more than larger ones. This size dependence is crucial in predicting the motion of particles under the influence of radiation forces.

Radiation Pressure

Radiation pressure is the force exerted by electromagnetic radiation when it transfers momentum to matter. In astrophysical contexts, this force becomes significant for small particles, as photons from a star impart momentum upon absorption or reflection, influencing the motion of dust or gas in space.

Force Balance in Particle Dynamics

Understanding particle dynamics in space requires considering the balance between different forces, such as gravitational attraction and radiation pressure. This balance determines the trajectory of particles, where the net force acting on a particle influences whether it follows a straight path or a curved one.

Transcript

00:01 So in this situation, we have a particle far away from the sun, and we want to know the residual force that it applies to know what direction of the tail of the comet is pointing at.

00:23 So a distance away from the sun, let's call this distance r, capital r.

00:34 We have the pull of gravity, but also the sun is radiating away.

00:39 And so there is a radiation pressure, is there anything a force in this particle that we assume to be spherical? we just need to know each one of these forces and then see when they are, combine when they cancel out to know the limit between the the place where the gravity wins and the limit where the radiation pressure wins.

01:09 So first the force of the radiation is just the intensity times the cross -sectional area divided by c.

01:22 So we are assuming a spherical particle so the area cross -sectional area will be pi r square so this is the intensity is the pressure the power of the sun divided by the distance away so this intensity is power of the sun divided by four pi r square and the cross -section area is pi r square divided by c so we can just simplify a little little bit.

02:13 So this is power of the sun, radius of the sphere divided by 4r square c.

02:24 Now the force of gravity is just the newton's constant, the mass of this sum, mass of this particle divided by the distance away, this r square.

02:41 So this is, we can write the mass in terms of the density because we we are assuming that is a sphere and the volume of sphere is four thirds of pi r q so this is gm s divided by r square times four pi r q divided by three and we can write this as four pi gms gms rule so this we have a row here because we are writing the mass as density times volume.

03:26 R cube divided by 3r square.

03:36 Now we want to know what radius this happens.

03:43 So let's find out the condition where fr is equal to fg...

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