Minimum Distance Between Earth & Mars: Analytic Calc

In summary, the minimum distance between Earth and Mars during their rotation in orbits is approximately 55.7 million km. This can be roughly calculated by subtracting Mars' perihelion from Earth's semi-major axis. For a more accurate value, one would need to consider Earth's eccentricity and the relative orientation of the ellipses.
  • #1
deltasata
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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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  • #2


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.
 

1. What is the minimum distance between Earth and Mars?

The minimum distance between Earth and Mars varies, as both planets orbit the sun in elliptical paths. However, the closest possible distance between the two planets is about 33.9 million miles (54.6 million kilometers). This occurs when the two planets are at their closest points in their respective orbits, a phenomenon called opposition.

2. How often does the minimum distance between Earth and Mars occur?

The minimum distance between Earth and Mars occurs approximately every 26 months, due to the difference in the length of Earth's and Mars' orbits around the sun. This alignment of the two planets is what allows for spacecraft to be sent from Earth to Mars with the shortest possible travel time.

3. Is the minimum distance between Earth and Mars the same every time?

No, the minimum distance between Earth and Mars varies with each opposition. This is because both planets have slightly different orbital paths, and their closest points to each other will differ from opposition to opposition.

4. How long does it take to travel from Earth to Mars during the minimum distance?

The minimum distance between Earth and Mars is only one factor in determining the travel time between the two planets. The actual travel time can vary depending on the speed of the spacecraft, the alignment of the two planets, and the route taken. However, the minimum travel time is approximately 6-7 months, using current spacecraft technology.

5. What factors affect the minimum distance between Earth and Mars?

The minimum distance between Earth and Mars is primarily affected by the difference in the length of the two planets' orbits around the sun. This, combined with the varying speeds of the planets as they orbit, determines the closest possible distance between them. Other factors that can affect the minimum distance include the gravitational pull of other planets, known as planetary perturbations, and the varying inclinations of Earth's and Mars' orbits relative to each other.

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