Spectral shifts: a low-speed astronomical estimate
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| redshift/ˈredʃɪft/ | Đỏ dịch |
| rest wavelength/rest ˈweɪvleŋθ/ | B sóng nghỉ |
What would explain this observation?
- A recognizable spectral line appears at a longer wavelength in a distant source. Its shift can provide evidence of recession along the line of sight.
Build the model
- Relative source-observer motion changes observed frequency or wavelength.
- For light at a relative speed much smaller than c, the magnitude of the fractional wavelength shift is approximately v/c.
- Recession corresponds to longer wavelength, and approach to shorter wavelength.
- redshift 红移: Shift of an identified line toward longer wavelength.
- rest wavelength 静止波长: Wavelength of the line measured with no relative source motion.
What does an identified line shifting to a longer wavelength suggest in the stated model?
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A known line found at a longer wavelength is redshifted, which in this model means the source is receding along the line of sight. The speed of light is constant, and a shifted line still has a nonzero frequency.
Match each technical term to its precise meaning.
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Use the definitions to distinguish related quantities and processes.
Choose evidence that can test it
- Compare a identified line with its laboratory rest wavelength.
- Use z = (observed−rest)/rest, then v approximately cz in the stated low-speed model.
- Do not apply this approximation without checking the regime or treating a cosmological redshift as a simple exact velocity.
In the lab: Use attributed spectra with calibration and line identification. Compare several lines for a consistent shift. State uncertainty and distinguish relative line-of-sight motion from an unmeasured transverse component.
Which two habits make the investigation or model in this case more defensible?
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Stating the conditions and assumptions lets others repeat the work exactly, and recording the supporting evidence lets them check the conclusion. Hiding disagreeing results removes the evidence that could challenge a wrong conclusion, and one measurement can never establish a wider claim.
Work from known quantities
- Known: a 500 nm rest line is observed at 501 nm. z = (501−500)/500 = 0.002.
- With c=3.0×10⁸ m/s, v approximately 6.0×10⁵ m/s away.
- The sound-source denominator formula is not the required SL light approximation.
Your turn: A 600 nm rest line is observed at 601.2 nm. Find z=(observed−rest)/rest.
A 600 nm rest line is observed at 601.2 nm. Find z=(observed−rest)/rest.
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The result is 0.002 . Known: rest 600 nm; observed 601.2 nm. Use z = (observed - rest)/rest. z = (601.2 - 600)/600 = 0.002. Positive z is a redshift; at low speeds v is approximately cz.
Check the conclusion and its limits
- The approximate shift relation does not show that light travels faster from an approaching source.
- A single unidentified line cannot safely establish a redshift.
Not true: An observed redshift means light speed increased. Light speed in vacuum is the same for all observers. Redshift is a change in observed wavelength from relative motion (or expanding space), not light travelling faster or slower.
- Relative source-observer motion changes observed frequency or wavelength.
- Compare a identified line with its laboratory rest wavelength.
- Watch for: the approximate shift relation does not show that light travels faster from an approaching source.
Write from a redshift of 0.004
- A 400 nm rest line is observed at 401.6 nm.
- Find z. Redshift does not mean the speed of light increased.
An observed redshift means light speed increased.
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Light speed in vacuum is the same for all observers. Redshift is a change in observed wavelength from relative motion (or expanding space), not light travelling faster or slower.
Shift of an identified line toward longer wavelength: write the technical term.
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redshift means Shift of an identified line toward longer wavelength.
A 400 nm rest line is observed at 401.6 nm. What is z, and why does a redshift not mean the speed of light increased?
The fractional shift is the change in wavelength divided by the rest wavelength.
What is z?
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1.6 divided by 400 is 0.004. Other options — 0.002 (the lesson shift from 600 nm to 601.2 nm); 1.6 nm (the wavelength change).