Edexcel A Level (IAL) Physics-5.42 Standard Candles- Study Notes- New Syllabus
Edexcel A Level (IAL) Physics -5.42 Standard Candles- Study Notes- New syllabus
Edexcel A Level (IAL) Physics -5.42 Standard Candles- Study Notes -Edexcel A level Physics – per latest Syllabus.
Key Concepts:
Determining Astronomical Distances Using Standard Candles
Standard candles are astronomical objects whose luminosity is known. By measuring the intensity of radiation received from them, their distance can be calculated.
What Is a Standard Candle?
A standard candle is an object that:
- Has a known luminosity \( L \).
- Emits radiation uniformly in all directions.
- Can be used as a reference to measure distance.
Examples:
- Cepheid variable stars
- Type Ia supernovae
Intensity and the Inverse-Square Law
The intensity \( I \) received from a luminous source at distance \( d \) is:
\( I = \dfrac{L}{4\pi d^2} \)
- \( I \) = intensity received (W m⁻²)
- \( L \) = luminosity of the source (W)
- \( d \) = distance from the source (m)
Key idea:
- As distance increases, intensity decreases.
- This follows an inverse-square law.
Determining Distance Using a Standard Candle
If luminosity \( L \) is known and intensity \( I \) is measured:
\( d = \sqrt{\dfrac{L}{4\pi I}} \)
This allows astronomers to calculate distance directly.
Why Standard Candles Are Useful
- Can be seen at much greater distances than parallax allows.
- Extend the cosmic distance scale.
- Used to measure distances to other galaxies.
Important:
- The luminosity must be well-known.
- Interstellar absorption may reduce measured intensity.
Limitations of the Method
- Dust and gas can absorb radiation.
- Errors in luminosity lead to distance errors.
- Requires calibration using nearer objects.
Example (Easy)
A standard candle has luminosity \( 1.0\times10^{28}\,\mathrm{W} \). Calculate the intensity at a distance of \( 1.0\times10^{13}\,\mathrm{m} \).
▶️ Answer / Explanation
\( I = \dfrac{L}{4\pi d^2} \)
\( I = \dfrac{1.0\times10^{28}}{4\pi(1.0\times10^{13})^2} \)
\( I \approx 8.0\,\mathrm{W\,m^{-2}} \)
Example (Medium)
A Cepheid variable has luminosity \( 5.0\times10^{29}\,\mathrm{W} \). The intensity measured at Earth is \( 2.0\times10^{-10}\,\mathrm{W\,m^{-2}} \). Calculate the distance to the star.
▶️ Answer / Explanation
\( d = \sqrt{\dfrac{L}{4\pi I}} \)
\( d = \sqrt{\dfrac{5.0\times10^{29}}{4\pi(2.0\times10^{-10})}} \)
\( d \approx 4.5\times10^{19}\,\mathrm{m} \)
Example (Hard)
The measured intensity from a standard candle is four times smaller than expected. By what factor is the estimated distance wrong?
▶️ Answer / Explanation
Using inverse-square law:
\( I \propto \dfrac{1}{d^2} \)
If intensity is \( \dfrac{1}{4} \), distance increases by factor \( \sqrt{4} = 2 \)
The distance is overestimated by a factor of 2.