APOD: Mars in the Loop (2012 Aug 09)

[Anthony Barreiro]

Of course. With the amazing star background, it is easy to forget that the camera was pointed in a different direction for each picture so we are seeing a different part of the Mars plane, making the "up and down" motion understandable.

Regardless of exactly where the imager had his camera aimed, all the images have been registered against the star background, so effectively we are seeing in just one direction over the entire period of time. In fact, it's because the view isn't changing that we see that up and down motion so clearly.

Out of curiosity, what is the angle between the two planes and when during our year do they intersect?

Mars is inclined 1.85° to the ecliptic. To calculate the intersection dates, you need to look at the orbital elements for both Earth and Mars, specifically the longitude of the ascending node. Of course, the Earth crosses Mars's orbital plane exactly twice a year; by my calculation around May 10 and November 11. Obviously these crossings are almost exactly 6 months apart, given the very nearly circular orbit of the Earth.

I'm not that good at math. According to http://spider.seds.org/spider/Mars/mars2012.html , here are the nodes during the previous, current, and next apparitions of Mars (ascending node is when Mars passes from south to north of Earth's ecliptic plane, descending node is when Mars passes from north to south of Earth's ecliptic plane):
20 August 2009 ascending
7 September 2010 descending
8 July 2011 ascending
25 July 2012 descending
25 May 2013 ascending
11 June 2014 descending

[Chris Peterson]

Out of curiosity, what is the angle between the two planes and when during our year do they intersect?

Mars is inclined 1.85° to the ecliptic. To calculate the intersection dates, you need to look at the orbital elements for both Earth and Mars, specifically the longitude of the ascending node. Of course, the Earth crosses Mars's orbital plane exactly twice a year; by my calculation around May 10 and November 11. Obviously these crossings are almost exactly 6 months apart, given the very nearly circular orbit of the Earth.

I'm not that good at math. According to http://spider.seds.org/spider/Mars/mars2012.html , here are the nodes during the previous, current, and next apparitions of Mars (ascending node is when Mars passes from south to north of Earth's ecliptic plane, descending node is when Mars passes from north to south of Earth's ecliptic plane):
20 August 2009 ascending
7 September 2010 descending
8 July 2011 ascending
25 July 2012 descending
25 May 2013 ascending
11 June 2014 descending

Right, but we're talking about different things. The nodes define when Mars itself crosses the ecliptic, which happens about once a year (because of Mars's ~2 year orbit) and which depends on the position of Mars- so the Earth date changes. The question, however, was on what dates does the Earth cross the plane of Mars's orbit. That doesn't depend on the position of Mars at all, only the position of the Earth, and because the two planes are fixed (ignoring very long precession cycles), the dates don't change.

[Ann]

Interestingly, it was the orbit of Mars (as measured by Tycho Brahe) that made Johannes Kepler realize that the planets follow elliptical orbits around the Sun. The orbit of Mars is, incidentally, more elliptical than the orbit of the Earth.

Although your meaning is clear, it would be better to say "more eccentric" than "more elliptical", as eccentricity is the measure of how out-of-round an ellipse is (and even a circle is actually an ellipse).

Source: http://en.wikipedia.org/wiki/Eccentricity

An eccentric old lady, Madame de Meuron, with an elliptical hat and ear trumpet.



Ann

[Anthony Barreiro]

Right, but we're talking about different things. The nodes define when Mars itself crosses the ecliptic, which happens about once a year (because of Mars's ~2 year orbit) and which depends on the position of Mars- so the Earth date changes. The question, however, was on what dates does the Earth cross the plane of Mars's orbit. That doesn't depend on the position of Mars at all, only the position of the Earth, and because the two planes are fixed (ignoring very long precession cycles), the dates don't change.

We do seem to be talking about different things. Perhaps I misunderstood waterfeller's question. We had started talking about why Mars' path before and after opposition is a loop rather than a straight line. That has to do with Mars' apparent motion north and south relative to Earth's ecliptic plane, i.e. where Mars is relative the nodes. When an outer planet's opposition (or the inferior conjunction of an inner planet) is farther from the ecliptic (farther from a node) you get a loop, and when it's closer to the ecliptic (closer to a node) you get an S-shaped path.

[Chris Peterson]

We do seem to be talking about different things. Perhaps I misunderstood waterfeller's question. We had started talking about why Mars' path before and after opposition is a loop rather than a straight line. That has to do with Mars' apparent motion north and south relative to Earth's ecliptic plane, i.e. where Mars is relative the nodes. When an outer planet's opposition (or the inferior conjunction of an inner planet) is farther from the ecliptic (farther from a node) you get a loop, and when it's closer to the ecliptic (closer to a node) you get an S-shaped path.

Yes. The question is specifically when the planes intersect, which is better expressed as where the planes intersect. Obviously, two planes intersect in a line (which passes through the Sun). Earth will cross that line twice a year, always on the same dates and almost exactly 6 months apart. Mars will cross the line twice every Mars year, on the same Martian dates, but changing Earth dates. Since the line of intersection isn't along Mars's semimajor orbital axis, the two crossing dates are not evenly spaced in the Martian year (due to Mars's fairly eccentric orbit).

[Keyman]

When an outer planet's opposition (or the inferior conjunction of an inner planet) is farther from the ecliptic (farther from a node) you get a loop, and when it's closer to the ecliptic (closer to a node) you get an S-shaped path.

...so that when/if it's AT a node, you'd get the "line" waterfeller was envisioning?

[kilocharliemike]

What an amazing series! And thanks for the one sentence explanation of retrograde motion, very helpful!

[ta152h0]

Is this the same process the smart ones use to determine if stars have planets orbiting, " the wobble " ?

[Chris Peterson]

Is this the same process the smart ones use to determine if stars have planets orbiting, " the wobble " ?

No. Stars that wobble because of their planets are examined spectroscopically, since the wobble introduces Doppler shift.

[Anthony Barreiro]

When an outer planet's opposition (or the inferior conjunction of an inner planet) is farther from the ecliptic (farther from a node) you get a loop, and when it's closer to the ecliptic (closer to a node) you get an S-shaped path.

...so that when/if it's AT a node, you'd get the "line" waterfeller was envisioning?

Yes, almost. When an outer planet is at opposition at the same time that it is crossing Earth's ecliptic plane (i.e. at one of its nodes) it will follow an S-shaped path that is so shallow that it will be virtually indistinguishable from a straight line. The same will be true for an inner planet that reaches inferior conjunction at the same time it crosses Earth's ecliptic plane.