- #1
Andrev
- 17
- 0
Hi!
The light variation of a Cepheid is 2 mag,if its effective temperature at maximum luminosity is
6000K, while at minimum is 5000K, please estimate the ratio of its maximum and minimum
radius.
$$\Delta m=-2,5lg\frac{L_{min}}{L_{max}}$$
$$lg\frac{L_{min}}{L_{max}}=2lg\frac{R_{min}}{R_{max}}+4lg\frac{L_{min}}{L_{max}}$$
Well, actually I should solve the problem with those two formulas above. My question is: why I can not just calculate the $$\frac{L_{min}}{L_{max}}$$ and solve the $$\frac{L_{min}}{L_{max}}=\frac{4\pi R_{min}^2 \cdot T_{min}^4\cdot \sigma}{4\pi R_{max}^2 \cdot T_{max}^4\cdot \sigma}$$ equation? Why I have to calculate with the lgs? As I studied the problem it looked for me that these two methods are equal but I got different results.
Thanks in advance,
Andrev
Homework Statement
The light variation of a Cepheid is 2 mag,if its effective temperature at maximum luminosity is
6000K, while at minimum is 5000K, please estimate the ratio of its maximum and minimum
radius.
Homework Equations
$$\Delta m=-2,5lg\frac{L_{min}}{L_{max}}$$
$$lg\frac{L_{min}}{L_{max}}=2lg\frac{R_{min}}{R_{max}}+4lg\frac{L_{min}}{L_{max}}$$
The Attempt at a Solution
Well, actually I should solve the problem with those two formulas above. My question is: why I can not just calculate the $$\frac{L_{min}}{L_{max}}$$ and solve the $$\frac{L_{min}}{L_{max}}=\frac{4\pi R_{min}^2 \cdot T_{min}^4\cdot \sigma}{4\pi R_{max}^2 \cdot T_{max}^4\cdot \sigma}$$ equation? Why I have to calculate with the lgs? As I studied the problem it looked for me that these two methods are equal but I got different results.
Thanks in advance,
Andrev