Ten points to anyone who can help me solve this!!?

Astronomers are currently searching for planets orbiting around other stars; they have found over 400 “extrasolar" planets since the first one was discovered in 1995. In order to better understand foreign planetary systems, astronomers attempt to learn everything they can about our solar system. One of the most obvious features of our solar system is that the four inner planets are almost entirely composed of rock and metals, while the outer planets are mostly gas and ice (which is frozen gas). To explain this distribution of matter, astronomers look to the time before the

planets formed.

When our sun was first “born”, astronomers believe that it was orbited by a large disk of gas and dust that would eventually coalesce to form the planets. Before the planets formed, however, the matter in this disk would separate due to the competing forces of the gravitational pull of the sun and the outward push due to the radiation pressure of the sun’s light. To understand how these forces could cause the gas and dust to separate, assume that a dust particle is made of larger atoms and has an average density of 2500 kg/m3 and a gas particle (frozen or not) has an average density of 800 kg/m3.

Consider a particle (could be either gas or dust) of radius R and with a reflectivity coefficient of a (note that a varies from 1 to 2... totally reflective means a = 2, totally absorbent means a = 1. You will use a when you write the radiation pressure.) If this particle is at a distance r from the sun:

 Derive an expression for the inward gravitational force on the particle due to the sun, in terms of R, r, M (the mass of the sun), and r (the density of the particle).

 Derive an expression for the outward force on the particle due to the radiation pressure of the sun’s light, in terms of P (the total power output of the sun), r, R and a. (Note: be very careful when considering the area of the particle on which the radiation acts. It is NOT 2pr2.)

 Combine the two expressions to create an expression for the total force. Write the expression so that a positive total force points toward the sun.

 First two questions: what direction is the total force if R is very large? Examine the place of R in each term of the total force. What direction is the total force if R is very small?

 Set the total force to zero and solve for R. This is the radius of a particle for which the two forces are balanced. If a particle has a radius greater than this value, it should be pulled inward; if its radius is smaller than this value, it should be pushed outward.

 Using the values: M = 1.99 x 1030 kg P = 3.9 x 1026 W

Calculate the value of R for which the force is zero for:

 a gas particle for which a is 2 (we assume gas particles will be totally reflective)

 a dust particle for which a is 1 (we assume dust particles are totally absorbent)

 From your answers to the calculations, where do we expect that most of the gas in the early solar system ended up... inward or outward? Where should most of the dust ended up? Explain how your answers relate to the value of R you calculated.