Minimum Distance Between Earth & Mars: Analytic Calc

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SUMMARY

The minimum distance between Earth and Mars, assuming co-planar orbits, is approximately 55.7 million kilometers. This value is derived by subtracting Mars' perihelion (206,669,000 km) from Earth's semi-major axis (149,598,261 km), resulting in a rough approximation of 57 million kilometers. For a more accurate calculation, one must consider Earth's orbital eccentricity and the relative orientation of the elliptical orbits of both planets.

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  • Understanding of orbital mechanics
  • Familiarity with planetary distances and measurements
  • Knowledge of eccentricity in elliptical orbits
  • Basic calculus for analytic derivation
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  • Research the concept of orbital eccentricity in planetary orbits
  • Study the analytic methods for calculating distances in celestial mechanics
  • Explore the implications of co-planar versus non-co-planar orbits
  • Learn about the historical minimum distances between Earth and Mars
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What is the minimum distance between Earth and Mars in course of their rotation in orbits?
I need the derivation and analytic calculation.
If we assume the plane of rotation is different for Earth and mars, the problem become to complicated. So the orbits may be assumed co-planner.Please provide me some useful links...
 
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The minimal distance when? Within the next 100 years, or within geological timescales?

55.7 million km

You get a rough approximation by subtracting mars' perihelion and Earth's semi-major axis:
Earth 149,598,261 km
Mars 206,669,000 km
Difference 57 million km.

A better value would require to look at Earth's eccentricity and the relative orientation of the ellipses.
 

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