Overview
This lecture explains how astronomers determine a star’s luminosity (true brightness) and distinguishes it from apparent brightness, focusing on their relationship with distance.
Measuring Distance
- Assume we know the distance to every star using parallax or other methods for this discussion.
- Knowing distance is essential to determining other stellar properties.
Luminosity
- Luminosity is the total amount of light energy a star emits per second in all directions.
- Denoted with a capital L.
- Luminosity is an indirect property; we cannot measure it directly because light radiates in every direction.
- To measure luminosity directly, one would need to capture all emitted light from every angle, which isn't possible.
Apparent Brightness
- Apparent brightness is the amount of a star's light that reaches us.
- Denoted with a lowercase b.
- It is a direct measurement; we observe how bright the star appears from Earth.
- Apparent brightness depends on both luminosity and the star’s distance from us.
Relationship Between Luminosity, Apparent Brightness, and Distance
- Light from a star spreads out as it travels, so objects farther away appear dimmer.
- The farther you are, the less light reaches you, as it spreads over a larger area.
- Apparent brightness increases with higher luminosity and decreases as distance increases.
The Brightness Equation
- The relationship is: B = L / (4πd²)
- B = apparent brightness; L = luminosity; d = distance to the star.
- Increasing L increases B; increasing d decreases B.
- The denominator (4πd²) is the surface area of a sphere (the spreading of light).
Using the Brightness Equation
- Astronomers already know the distance and can directly measure apparent brightness.
- To calculate luminosity, rearrange: L = 4πd²B.
- To find a star's luminosity, an astronomer must know both its distance and apparent brightness.
Key Terms & Definitions
- Luminosity (L) — Total amount of light energy a star emits per second in all directions.
- Apparent Brightness (B) — The observed brightness of a star as seen from Earth.
- Distance (d) — The space between the observer and the star, often measured using parallax.
- 4πd² — Surface area of a sphere, representing the area over which the star’s light spreads.
Action Items / Next Steps
- Review the relationship between luminosity, apparent brightness, and distance.
- Be prepared to answer questions on what is needed to determine a star’s luminosity (distance and apparent brightness).