Earth Science, Astronomy, Space / Principles and Exploration
Stellar temperature, radius, and luminosity — principles and investigation
The energy a star produces itself and how bright it appears from Earth are two different amounts. Compare the luminous intensity and apparent brightness by changing the surface temperature, radius, and distance one by one. The key point is that temperature and size change the luminosity, but changes in distance only change the observed brightness.
How does it work?
Doubling the temperature is 16 times the luminosity, and doubling the radius is 4 times the luminosity. Distance does not change luminosity.
L/L☉=(R/R☉)²(T/5778)⁴ · λmax=2.898×10⁶/T nm
Try this investigation
- Compare the star color and size of the two stars by adjusting the temperature, radius, and distance. Execution is a process of observing certain conditions and passing time.
- Record stars with twice the solar conditions and temperature. Check the shift of the peak of the Planck curve and the change in luminosity.
- We distinguish between luminous intensity and apparent brightness by adding the conditions of doubling the radius and doubling the distance.
Interpreting your results
What changes if the same star moves twice as far away?
The luminosity L is the amount of emission of the star itself. The apparent brightness is proportional to L/d², so when the distance is doubled, it becomes 1/4.
Assumptions and limitations
Assume the star is a black body of uniform temperature. T☉=5778 K, use the Wien’s displacement constant 2.898×10⁻³ m·K. Apparent brightness is a relative value of L/d², omitting the common 1/(4π). The colors are approximations for the screen based on temperature, and the radius plot is logarithmic scale. Interstellar extinction, absorption lines, and stellar evolution paths are not calculated.