You learned wrong.
It is not.
Numbers are all there is. You offer 43 minutes and 11 minutes and other numbers but I think you are confused about what those numbers are telling us about the speed of light. We need to ensure were all talking about the same scenario.
You brought this to a discussion forum, presumably to discuss it. If we can't discuss a common scenario, then there is little discussion to be had, beyond "You've misunderstood something somewhere, but we can't tell you where".
Ole Rømer's most significant measurement was his estimation of the speed of light, derived from observations of the eclipses of Jupiter's moon Io. Below, I’ll detail the specific measurements he recorded and how he used them to calculate the speed of light, as well as any other relevant measurements from his work. Since his primary contribution in this context is the speed of light, I’ll focus on that, but I’ll also touch on other measurements he made where data is available, based on historical records.
1. Measurement of the Speed of Light (1676)
Context:Rømer observed the eclipses of Io, one of Jupiter’s moons, while working at the Paris Observatory. He noticed that the timing of Io’s eclipses (when it passed into Jupiter’s shadow) varied depending on Earth’s position relative to Jupiter.
Specific Measurements:
- Orbital Period of Io: Rømer determined that Io’s orbital period around Jupiter was approximately 42.5 hours (modern value: ~42.46 hours, or 1.769 days). This was based on repeated observations of Io’s eclipses.
- Time Discrepancies: Rømer tracked the timing of Io’s eclipses over several months in 1675–1676. He found that:
- When Earth was closer to Jupiter (at opposition), the eclipses occurred earlier than predicted.
- When Earth was farther from Jupiter (at conjunction), the eclipses were delayed.
- The maximum observed delay between successive eclipses accumulated to approximately 22 minutes (1,320 seconds) when Earth moved from its closest to its farthest point from Jupiter (i.e., across the diameter of Earth’s orbit, about 2 astronomical units or AU).
- Earth’s Orbital Diameter: At the time, the size of Earth’s orbit was estimated using the astronomical unit (AU), the average distance from Earth to the Sun. The best estimate available to Rømer, based on work by astronomers like Cassini and Kepler, was that the diameter of Earth’s orbit was approximately 186 million miles (modern value: ~186 million miles or 300 million kilometers).
Calculation:Rømer hypothesized that the 22-minute delay was due to the time it took light to travel across the diameter of Earth’s orbit. Using the formula:
Speed of light=DistanceTime \text{Speed of light} = \frac{\text{Distance}}{\text{Time}} Speed of light=TimeDistance
- Distance: Diameter of Earth’s orbit ≈ 186 million miles (or ~300 million kilometers, though Rømer used units based on the French lieue or miles of the time).
- Time: ~1,320 seconds (22 minutes).
Rømer calculated the speed of light as approximately
220,000 kilometers per second (or about 136,700 miles per second). This was roughly 26% lower than the modern value of 299,792 km/s, primarily due to inaccuracies in the estimated size of Earth’s orbit and the exact time delay.
Data Source:Rømer presented these findings in a brief paper to the French Academy of Sciences, published in the
Journal des sçavans on December 7, 1676. His observations were based on data collected over several months, comparing predicted versus observed eclipse times. The exact dataset (e.g., specific eclipse timings) is not fully preserved, as many of Rømer’s records were lost in the 1728 Copenhagen fire, but his conclusion of a 22-minute delay is well-documented.
2. Other Astronomical Measurements
While Rømer’s speed-of-light work is the most detailed measurement recorded, he also made precise measurements in other areas of astronomy:
- Jupiter’s Moons:
- Rømer compiled detailed tables of the orbital periods of Jupiter’s Galilean moons (Io, Europa, Ganymede, Callisto). For example:
- Io: ~42.5 hours (1.77 days).
- Europa: ~85.2 hours (3.55 days).
- Ganymede: ~171.7 hours (7.15 days).
- Callisto: ~400.5 hours (16.69 days).
- These measurements were derived zet from repeated observations of eclipse timings and were accurate enough to be used for navigation and longitude determination.
- Star Positions:
- At the Paris Observatory, Rømer used a meridian telescope to measure the angular positions of stars relative to the meridian. His measurements contributed to star catalogues, with positional accuracies on the order of arcminutes (e.g., within 1–2 arcminutes, or ~0.017–0.033 degrees), limited by the instruments of the time.
- Specific numerical data for individual stars are not well-preserved, but his work supported the broader efforts of the observatory to map celestial coordinates.
- Lunar and Solar Observations:
- Rømer recorded timings of lunar eclipses and solar phenomena, such as transits and sunspot observations. These measurements helped refine ephemerides, but exact numerical values are sparse in surviving records.
- For example, he measured the timing of lunar eclipses to within a few minutes, contributing to tables predicting celestial events.
3. Thermometry: The Rømer Scale
Rømer developed an early temperature scale, one of the first to use fixed reference points. His measurements included:
- 0° Rømer: The freezing point of a brine solution (a mixture of water and salt), approximately -14°C in modern terms.
- 7.5° Rømer: The freezing point of pure water (0°C).
- 60° Rømer: The boiling point of water at standard pressure (~100°C).
These reference points were based on experimental measurements using alcohol-based thermometers, which Rømer calibrated himself. While not widely adopted, his scale influenced Daniel Fahrenheit’s later work.
4. Limitations and Missing Data
- Lost Records: Many of Rømer’s detailed observational records, including specific eclipse timings and instrument measurements, were destroyed in the 1728 Copenhagen fire. This makes it challenging to reconstruct exact datasets beyond what was published or referenced by contemporaries like Huygens and Newton.
- Instrument Precision: Rømer’s measurements were limited by the technology of the time. For example, his telescopes and clocks had accuracies of a few arcminutes and seconds, respectively, which introduced small errors into his calculations.
- Astronomical Unit Uncertainty: The size of Earth’s orbit was not precisely known in Rømer’s time, leading to an underestimate of the speed of light. Modern calculations, using his 22-minute delay and the correct orbital diameter (~300 million km), yield a closer approximation to the true speed.
Summary of Key Measurements
- Speed of Light:
- Observed delay in Io’s eclipses: ~22 minutes (1,320 seconds) across Earth’s orbit.
- Estimated orbital diameter: ~186 million miles (~300 million km).
- Calculated speed: ~220,000 km/s.
- Io’s Orbital Period: ~42.5 hours.
- Other Moons: Accurate periods for Europa (~85.2 hours), Ganymede (~171.7 hours), and Callisto (~400.5 hours).
- Star Positions: Angular measurements within ~1–2 arcminutes.
- Temperature Scale: 0° (brine freezing), 7.5° (water freezing), 60° (water boiling).
Rømer’s measurements were remarkable for their time, achieved with rudimentary instruments and limited computational tools. His work on the speed of light, in particular, relied on meticulous observation and innovative reasoning, marking a turning point in the understanding of light’s properties. If you’d like me to focus on a specific measurement or attempt to reconstruct a dataset (e.g., using modern values to simulate Rømer’s calculations), let me know!
