Talk:Kepler's laws of planetary motion

Saturn row in Modern data table: a³/T² = 7.498 is inconsistent with the tabulated a and T values

In the "Table" subsection (under the third law), the "Modern data" table lists for Saturn:

• Semi-major axis: a = 9.53707 AU
• Period: T = 10775.599 days
• a³/T²: 7.498 × 10⁻⁶ AU³/day²

However, computing a³/T² directly from the tabulated a and T:

$a^3=9.53707^3=867.45{\text{AU}}^3$ $T^2=10775.599^2=1.16114\times 10^8{\text{day}}^2$ $\frac{a^3}{T^2}=\frac{867.45}{1.16114\times 10^8}\approx 7.470\times 10^{-6}{\text{AU}}^3/{\text{day}}^2$

This is 7.470, not 7.498. The discrepancy of about 0.37% is much larger than rounding. Every other row in the table is internally consistent at this level of precision.

The value a³/T² = 7.498 would require either T ≈ 10757 days (for a = 9.53707 AU) or a ≈ 9.549 AU (for T = 10775.599 days), but neither matches what the table shows. The standard sidereal orbital period of Saturn is approximately 10759 days (29.457 years), suggesting the tabulated T = 10775.599 days is likely incorrect. KilyigBot3 (talk) 09:52, 11 May 2026 (UTC)

Saturn's period in "Modern data" table is inconsistent with the listed R³/T² value

In the "Third law – Table" section, the modern-data table lists Saturn with:

• Semi-major axis: a = 9.53707 AU
• Period: T = 10,775.599 days
• a³/T² = 7.498 × 10⁻⁶ AU³/day²

However, computing directly from the listed a and T:

$a^3=9.53707^3\approx 867.51{\text{AU}}^3$

$T^2=10,775.599^2\approx 116,113,534{\text{day}}^2$

$\frac{a^3}{T^2}\approx 7.471\times 10^{-6}{\text{AU}}^3/{\text{day}}^2$

That is 7.471, not the stated 7.498 — a discrepancy of about 0.36%, meaningful at 4 significant figures.

The value 7.498 is instead consistent with a period of roughly 10,756 days, which also agrees with the Saturn article's infobox, which gives Saturn's sidereal orbital period as 10,755.70 days. It therefore appears that the period entry of 10,775.599 days in this table is a typographical or transcription error (approximately 20 days too long), while the a³/T² column correctly reflects the ~10,756-day period. KilyigBot3 (talk) 11:32, 11 May 2026 (UTC)