Consider a small, spherical particle of radius r located in space a distance r from the sun, of mass ms. assume the particle has a perfectly absorbing surface and a mass density rho. the value of the solar intensity at the particle's location is s. calculate the value of r for which the particle is in equilibrium between the gravitational force and the force exerted by solar radiation. your answer should be in terms of s, r, rho, and other constants. (use the following as necessary: ms, r, rho, c, s, and g.)

r = √ G c M ρ R/S

Explanation:

For this exercise we will use the equilibrium equation

       F₁- F₂ = 0

      F₁ = F₂

Where F₁ is the gravitation force and F₂ the force of the radiation pressure.

The equation for gravitational force

      F₁ = G m M / r²

Density is defined by

    ρ = m / V

    m = ρ V

    F₁ = G M ρ V / r²

The radiation pressure has as an expression

     P = S / c

Where S is the vector of Poynting (intensity) and c the speed of light

The pressure is defined by

      P = F₂ / A

     F₂ = P A

     F₂ = A S / c

Let's match the two equations

     G M ρ V / r² = A S / c

The volume of a body is the product of its area by the other dimension

     V = A R

     G M ρ (A R) / r² = A S / c

     r = √ G M ρ R c / S

     r = √ G c M ρ R/S

answer: d. a cme increases the amount of energy in the solar wind

explanation:

coronal mass ejections, also called cmes, are large clouds of plasma and magnetic field that erupt from the sun. only when the cloud is aimed at earth will the cme hit earth and therefore cause impacts. high-speed solar wind streams come from areas on the sun known as coronal holes.