 ## Mars Opposition query

• albertw
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• IFAS Secretary
• • Posts: 4173

### Mars Opposition query was created by albertw

Hi,

I've been looking into the details of the Mars opposition, and a few
articles I've seen basically claim that Earth and Mars would get
closest together when opposition occurs at the same time Mars is at
perihelion.

This seems basically right, but not exact.

Basically my problem is that I dont see why the minimum distance
between the two planets orbits should occur at exactly the perihelion
point of Mars orbit. It's bound to be close to it, but since the Earth
will be getting closer the Sun at that point (Earths perihelion is in
early July), isn't the closest point between the two orbits a little
before Mars perihelion? Put another way, why is the point where Mars
is closest to the sun the same as where its closest to the Earths
orbit? Or put (yet another but final!) way, why should the minimum
distance between two elipses that only share one common focus occur at
the perihelion point of the outer ellipse?

Perhaps I'm taking what I've read too literally, as I imagine the
difference would only be hours. But still It sounds easy to check, though I havent worked it out yet.

1. Based on say 2000.0 orbit data, calculate the minimum distance
between the two orbits. And hence at what point in Mars orbit does
this occur. This may even require that the relative inclination of the
orbits be taken into account (and that would require me learning more
maths!).

2. Compare this point with the perihelion point.

I'll sit down and try to calculate it at some point, but thought I'd
ask here in case there is a simple answer. Its a classic maths class
case of "I think I'm right but I cant prove it Sir!" Cheers,
~Al
Albert White MSc FRAS
Chairperson, International Dark Sky Association - Irish Section
www.darksky.ie/
19 years 6 months ago

• michaeloconnell
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• IFAS Astronomer of the Year 2009
• • Posts: 6319
The way I look at is that earth's orbit is an ellipse, but it's shape is almost identical to that of a circle. Mars's orbit shape however is a very defined ellipse. The distance between the two at mars opposition is proportional to the eccentricity of earth's orbit and the eccentricity of mars' orbit. However, the eccentricity of earth's orbit is miniscule to the the eccentricity of mars' orbit, therefore, mars is closest to earth when it is closest to the sun assuming the earth's orbit is a circle. However, as you correctly pointed out, earth's orbit is an ellipse so opposition and closest approach do not occur exactly the same time. To answer you question, mars is closest to earth on the 27 August 2003 at 09:51:12. It's at opposition on the 28th August 2003 at 17:59:02. It's distance at closest approach is 0.3727183 AU (Light time 0h 03m 06.0s ) while it's distance at opposition is 0.3728466 AU (Light time 0h 03m 06.1s ). As you can see I was busy with my calculator! .