Ptolemaic model

[chatgpt]

I’m looking at the famous Ptolemaic earth centric diagram. The earth is at the center, then we have the Moon, Mercury and Venus, the Sun, Mars, Jupiter and Saturn. Do we have the exact distances of the planets from the earth? And their periods? If so can you list distances and periods?

The Ptolemaic model, being geocentric, does not use modern concepts of absolute distances or accurate periods as we understand them today. Instead, it focused on relative distances and periods based on celestial observations. Nevertheless, the following provides an outline based on the Ptolemaic framework as well as approximate relative information that was utilized in such models:

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Ptolemaic Model (Geocentric Framework)

  1. Moon
    • Distance: Closest to Earth in the heavens (distance often unquantified, considered relative).
    • Period: Approximately 27.3 days (sidereal month).
  2. Mercury
    • Distance: Between Moon and Venus, closer to Earth than Venus.
    • Period: ~88 days (approximation of sidereal period).
  3. Venus
    • Distance: Beyond Mercury.
    • Period: ~225 days (sidereal period).
  4. Sun
    • Distance: Between Venus and Mars.
    • Period: ~1 year (365.25 days).
  5. Mars
    • Distance: Beyond the Sun.
    • Period: ~687 days (sidereal period).
  6. Jupiter
    • Distance: Beyond Mars.
    • Period: ~12 years (sidereal period).
  7. Saturn
    • Distance: Outermost celestial body in the Ptolemaic model.
    • Period: ~29.5 years (sidereal period).

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Relative Distances in Ptolemaic Terms

The Ptolemaic system did not express distances in modern units (e.g., kilometers or AU) but rather in ratios or geometrical frameworks using epicycles and deferents to explain retrograde motion and apparent changes in brightness.

For reference:

  • The distances were proportional to the spheres containing the celestial objects.
  • The system was qualitative rather than quantitative in precise distances.

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Modern Comparison

If you’re interested in the actual distances and periods, here’s a modern comparison for contrast:

  1. Moon:
    • Distance: ~384,400 km.
    • Period: 27.3 days.
  2. Mercury:
    • Distance: ~57.91 million km (0.39 AU).
    • Period: 87.97 days.
  3. Venus:
    • Distance: ~108.2 million km (0.72 AU).
    • Period: 224.7 days.
  4. Sun:
    • Distance: ~149.6 million km (1 AU).
    • Period: Apparent yearly motion due to Earth’s orbit.
  5. Mars:
    • Distance: ~227.9 million km (1.52 AU).
    • Period: 686.98 days.
  6. Jupiter:
    • Distance: ~778.5 million km (5.2 AU).
    • Period: 11.86 years.
  7. Saturn:
    • Distance: ~1.429 billion km (9.58 AU).
    • Period: 29.46 years.

Let me know if you’d like further details on either the Ptolemaic or modern astronomical distances and periods!

Ok. Are these distances between the earth and planets?

No, the distances listed in the “Modern Comparison” section are the average distances between the Sun and the planets, not the distances between Earth and the planets.

Earth-Planet Distances (Modern)

For the average distance between Earth and the planets, we use the concept of Astronomical Units (AU) and consider the planets’ orbits. Here’s a breakdown of the average distances between Earth and each celestial object:

  1. Moon:
    • Average Distance: ~384,400 km.
  2. Mercury:
    • Closest Approach (Perihelic Opposition): ~77 million km (~0.39 AU).
    • Average Distance: ~92 million km (~0.61 AU).
  3. Venus:
    • Closest Approach: ~38 million km (~0.28 AU).
    • Average Distance: ~41 million km (~0.28 AU).
  4. Mars:
    • Closest Approach: ~54.6 million km (~0.37 AU).
    • Average Distance: ~78 million km (~0.52 AU).
  5. Jupiter:
    • Closest Approach: ~588 million km (~3.93 AU).
    • Average Distance: ~628 million km (~4.2 AU).
  6. Saturn:
    • Closest Approach: ~1.2 billion km (~8.0 AU).
    • Average Distance: ~1.3 billion km (~8.54 AU).

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If you are looking for detailed numbers at specific moments (e.g., during closest approaches or oppositions), I can calculate these for particular scenarios. Let me know how you’d like to proceed!

Some sources give 77 million km as the average distance from the earth, not as the closest approach. Which one is correct?

The confusion arises because the average distance between Earth and Mercury is often misunderstood or inconsistently reported. Here’s a clarification:

Mercury’s Average Distance from Earth

The value of ~77 million kilometers (0.39 AU) is indeed the average distance between Earth and Mercury, not the closest approach. Mercury’s closest approach to Earth during inferior conjunction (when Mercury is between Earth and the Sun) is approximately 77 million kilometers. Since Mercury’s orbit is highly elliptical, its distance varies significantly.

### Key Distances for Mercury

  • Closest Approach (Inferior Conjunction): ~77 million km (~0.39 AU).
  • Farthest Distance (Superior Conjunction): ~222 million km (~1.48 AU).
  • Average Distance: ~91 million km (~0.61 AU) as calculated over time.

The variation in reported values (e.g., 77 million km as “average”) could come from different methods of calculating averages or approximations in older references.

Let me know if you want more details or an explanation of how these averages are calculated!

Created: 2025-01-29 Wed 10:51

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