- #1
cyberdiver
- 23
- 3
This is not actually a homework assignment, but something I decided to try in my own time. I wanted to find the radius from a star at which a solar sail would be held at equilibrium (radiation pressure = gravity), given mass per unit area and stellar luminosity at a reference radius.
So I attempted the following:
Pressure of radiation and pressure of gravity are equal and opposing:
[tex]p_{radiation}=-p_{gravity}[/tex]
Subsititute radiation pressure equation and gravity equation (rho_A is areal density, E_F is energy flux):
[tex]2 \cdot \frac{E_F}{c} = -{\rho}_A \cdot g[/tex]
Substitute inverse square law equation into E_F, areal density equation into rho_A, and the law of universal gravitation equation:
[tex]2 \cdot \frac{E_{F0} \cdot (\frac{r_0}{r})^2}{c} = -\frac{m}{A} \cdot \frac{G \cdot M}{r^2}[/tex]
Attempt to make r^2 the subject:
[tex]2 \cdot E_{F0} \cdot \frac{r_0^2}{r^2} \cdot A \cdot r^2 = -m \cdot G \cdot M[/tex]
The problem here is that r^2 and r^2 will cancel out, making the equation useless. How else could I solve this problem? Does it require calculus?
So I attempted the following:
Pressure of radiation and pressure of gravity are equal and opposing:
[tex]p_{radiation}=-p_{gravity}[/tex]
Subsititute radiation pressure equation and gravity equation (rho_A is areal density, E_F is energy flux):
[tex]2 \cdot \frac{E_F}{c} = -{\rho}_A \cdot g[/tex]
Substitute inverse square law equation into E_F, areal density equation into rho_A, and the law of universal gravitation equation:
[tex]2 \cdot \frac{E_{F0} \cdot (\frac{r_0}{r})^2}{c} = -\frac{m}{A} \cdot \frac{G \cdot M}{r^2}[/tex]
Attempt to make r^2 the subject:
[tex]2 \cdot E_{F0} \cdot \frac{r_0^2}{r^2} \cdot A \cdot r^2 = -m \cdot G \cdot M[/tex]
The problem here is that r^2 and r^2 will cancel out, making the equation useless. How else could I solve this problem? Does it require calculus?