How to measure the universe | The Cosmic Distance Ladder Part 2

Key Concepts:

• Cosmic Distance Ladder: A series of methods used to determine the distances to celestial objects.
• Parallax: The apparent shift in the position of an object when viewed from different locations.
• Transit of Venus: The event when Venus passes between the Sun and Earth, appearing as a small black dot moving across the Sun's disk.
• Astronomical Unit (AU): The average distance between the Earth and the Sun.
• Speed of Light: The speed at which light travels through a vacuum.
• Hertzsprung-Russell Diagram: A scatter plot of stars showing the relationship between their absolute magnitudes or luminosities versus their stellar classifications or effective temperatures.
• Main Sequence: A continuous and distinctive band of stars that appears on plots of stellar color versus brightness.
• Cepheid Variable Stars: Stars that pulsate radially, varying in both diameter and temperature and producing changes in brightness with a well-defined stable period and amplitude.
• Redshift: The displacement of spectral lines toward longer wavelengths (the red end of the spectrum) in the light emitted by distant celestial objects.
• Hubble's Law: The observation in cosmology that objects recede from Earth at a rate proportional to their distance.
• Standard Candle: An object with a known luminosity.
• Copernican Principle: The principle that the Earth is not in a central, specially favored position.

1. Measuring Distances within the Solar System using Parallax

• The Problem: Determining the exact scale of the Solar System after Kepler deduced the shapes of planetary orbits.
• Parallax Explained: Using the shift in an object's apparent position against background stars when viewed from different locations (like binocular vision).
• Earth-Based Observations: Measuring the position of a planet (e.g., Venus) from two distant points on Earth simultaneously.
• Trigonometry: Using the known distance between observation points on Earth and the measured angles to the planet to calculate the planet's distance.
• Challenges: The extremely small angles involved due to the vast distances. For Venus at its closest, the angle difference is about 1 arcminute (1/60th of a degree).
• Transit of Venus: Timing when Venus appears to touch the edge of the Sun from different locations to precisely measure the small angular difference.
• Duration Measurement: Observers measure the duration of the transit, which varies slightly due to parallax, allowing calculation of the angular separation.
• Example: Captain Cook's voyages included scientific missions to measure the transit of Venus.

2. The Story of Guillaume Le Gentil

• Le Gentil's Journey: An astronomer who spent years trying to observe the transit of Venus, first in 1761 and then in 1769.
• Misfortune: Missed the 1761 transit due to the Seven Years' War and the 1769 transit due to cloudy weather in the Philippines.
• Personal Cost: Upon returning to France, he was declared dead, his wife remarried, and his estate was plundered.

3. Determining the Speed of Light using Jupiter's Moon Io

• Romer's Observations: Observing the eclipses of Jupiter's moon Io as it passes into Jupiter's shadow.
• Inconsistent Timing: Noticing that the timing of Io's eclipses varied depending on Earth's position relative to Jupiter.
• Huygens's Realization: The variations were due to the time it takes light to travel the changing distance between Earth and Jupiter.
• Calculation: Light takes about 20 minutes to traverse the diameter of Earth's orbit (two astronomical units).
• Significance: Provided the first estimate of the speed of light, even before the precise measurement of the astronomical unit.
• Modern Relevance: Radar measurements of planetary distances rely on knowing the speed of light.

4. Measuring Distances to Nearby Stars using Parallax

• Earth's Orbit as Baseline: Using the Earth's orbit around the Sun as the baseline for parallax measurements.
• Six-Month Interval: Measuring a star's position at one point in Earth's orbit and then again six months later.
• Subtle Shift: The star's apparent position shifts slightly against the background of more distant stars.
• Proxima Centauri Example: A time-lapse shows the subtle drift of Proxima Centauri over six months.
• Small Angles: The parallax angle for even the closest star is extremely small (1.5 arcseconds for Proxima Centauri).
• Friedrich Bessel: Made the first successful parallax measurement of a star in 1838.

5. Determining Distances within the Milky Way using the Hertzsprung-Russell Diagram

• Limitations of Parallax: Parallax only works for relatively nearby stars.
• Inverse Square Law: The apparent brightness of a star decreases with the square of the distance.
• Hertzsprung-Russell Diagram: A plot of stars' absolute brightness versus color (or spectral type).
• Main Sequence: Most stars fall on the main sequence, a diagonal band on the H-R diagram.
• Harvard Computers: A group of women at the Harvard College Observatory who analyzed stellar spectra and contributed to the creation of the H-R diagram.
• Spectral Analysis: Analyzing the spectrum of a star to determine its composition and classify it.
• Standard Candle: Using the H-R diagram to estimate a star's absolute brightness based on its color and spectral type, then using the inverse square law to calculate its distance.

6. Measuring Intergalactic Distances using Cepheid Variable Stars

• Cepheid Variables: Supergiant stars whose brightness varies periodically.
• Period-Luminosity Relationship: Henrietta Swan Leavitt discovered that the period of a Cepheid's brightness variation is related to its absolute brightness.
• Standard Candle: Cepheid variables can be used as standard candles to measure distances to galaxies.
• Process: Measure the period of a Cepheid in a distant galaxy, use the period-luminosity relationship to determine its absolute brightness, and then use the inverse square law to calculate the distance to the galaxy.

7. Measuring Distances to Distant Galaxies using Redshift and Hubble's Law

• Redshift: The stretching of light waves from distant galaxies due to the expansion of the universe.
• Hubble's Law: The observation that the redshift of a galaxy is proportional to its distance.
• Edwin Hubble: Discovered Hubble's Law by measuring the redshifts and distances of galaxies.
• Process: Measure the redshift of a distant galaxy, and then use Hubble's Law to estimate its distance.
• Sloan Digital Sky Survey: A project that has mapped the positions and distances of millions of galaxies.
• Galaxy Filaments: Galaxies are not randomly distributed in space but form large-scale structures called filaments.

8. Gravitational Waves as Standard Sirens

• Black Hole Mergers: The collision of black holes releases a predictable amount of energy in the form of gravitational waves.
• Standard Sirens: The strength of the gravitational waves detected on Earth can be used to calculate the distance to the black hole merger.
• Cross-Checking: Gravitational wave distance measurements have been cross-checked against redshift measurements, with a 10% discrepancy.

9. The 10% Anomaly and the Copernican Principle

• Discrepancy: There is a 10% discrepancy between distance measurements based on Hubble's Law and other methods.
• Copernican Principle: The assumption that the laws of physics are the same throughout the universe.
• Ongoing Research: The cause of the 10% anomaly is an active area of research, potentially indicating a problem with our understanding of the universe.

10. Conclusion

The cosmic distance ladder is a complex and evolving system of methods used to measure the vast distances in the universe. Each rung of the ladder relies on the previous one, and each method has its limitations and uncertainties. Despite these challenges, astronomers have made remarkable progress in mapping the universe and understanding its structure and evolution. The ongoing 10% anomaly highlights that there are still mysteries to be solved and that our understanding of the universe is not yet complete.