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- Jun 12, 2018

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Two equal size bodies of the same mass can get much closer before reaching the Roche Limit. I used copilot to do the math for two earth size bodies of equal mass orbiting 20,000 miles apart. I figured copilot could do a better job tackling the math, which it did, but the explanation it gave in English didn't match the math. The math for this equation gets a lot simpler with equal size, equal mass bodies. If copilot is correct then

the Roche limit for two equal-sized bodies, such as Earth-sized planets, can be approximated by:

d≈2.44×R

where (R) is the radius of each planet. For Earth, the radius is about 6,371 kilometers. So, the Roche limit would be:

d≈2.44×6,371 km≈15,540 km

Since 20,000 miles is approximately 32,187 kilometers, this distance is well within the Roche limit. Therefore, the tidal forces would be extremely strong, and the planets would likely be torn apart.

If you have any more questions or need further clarification, feel free to ask!

I said copilot was wrong, and it replied:

The discrepancy occurred due to an error in my initial calculations and interpretation of the Roche limit. Here’s a breakdown of what happened:

Initial Calculation: I correctly calculated the Roche limit for two Earth-sized bodies using the formula (d \approx 2.44 \times R), where (R) is the radius of Earth (approximately 6,371 kilometers or 4,000 miles). This gave a Roche limit of approximately 15,540 kilometers (or 9,760 miles).

Conversion Error: When converting 20,000 miles to kilometers, I correctly noted that 20,000 miles is approximately 32,187 kilometers.

Misinterpretation: The error occurred when I incorrectly stated that 32,187 kilometers was within the Roche limit of 15,540 kilometers. In reality, 32,187 kilometers is well beyond the Roche limit, meaning the two Earth-sized bodies would not be torn apart at that distance.

I apologize for the confusion and any inconvenience caused by this mistake. Thank you for bringing it to my attention. If you have any more questions or need further clarification, feel free to ask!

According to copilot the earth moon would be traveling around the earth at 11,000 miles per hour. Going around a 120,000 mile orbit, it would take around 11 hours to do one orbit.