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This has been studied a lot. The evidence is showing that women sexually select both strong, highly-masculinated men at times, and more sensitive, less masculinated men at other times. For example:

Women's Preferences for Male Behavioral Displays Change Across the Menstrual Cycle.

Women prefer both the scent of symmetrical men and masculine male faces more during the fertile (late follicular and ovulatory) phases of their menstrual cycles than during their infertile (e.g., luteal) phases. Men's behavioral displays in social settings may convey signals that affect women's attraction to men even more strongly. This study examined shifts in women's preferences for these behavioral displays. A sample of 237 normally ovulating women viewed 36 or 40 videotaped men who were competing for a potential lunch date and then rated each man's attractiveness as a short-term and a long-term mate. As predicted, women's preference for men who displayed social presence and direct intrasexual competitiveness increased on high-fertility days relative to low-fertility days, but only in a short-term, not a long-term, mating context. These findings add to the growing literature indicating that women's mate preferences systematically vary across the reproductive cycle.

That's only in the current equilibrium, which is a highly simplified version of the general case.
That's why I said 'average distance'.

A flyby of a massive body (like Mars) could certainly affect Earth's orbit.
You'd think so, wouldn't you (I know I would). However, there are a couple of problems. The biggest one, of course, is arranging the fly-by. See previous comment involving unfeasible quantities of nuclear explosive.
More interesting is whether Mars counts as a 'massive body', and what it's effect on Earth would be.(All figures from NASA's Mars Fact Sheet). Let's do the maths :)

Mars has an orbital velocity of 24.13 km/s.
Earth's is 29.78 km/s.
Assuming we are trying to accelerate Mars, it can gain 5.65 km/s, which translates into a KE gain of c. 1E31 J.
Because energy is conserved, Earth must lose the same amount of KE, which, of course, will reduce its orbital velocity - but by how much?
Well, by the ancient formula, E=1/2mv^2, Earth has 5.9736E24kg/2*29780m/s^2 = 2.6488E33 J of KE.
Subtracting the KE 'stolen' by our wayward Martians, we are left with 'only' 2.6388E33 J, ie this transfer has cost Earth .01% of our total KE, giving a 0.1% reduction in orbital velocity.
What this would do to the length of a year I'm not sure (maybe somebody whose orbital mechanics is better than mine can tell us), but I doubt it would do more than annoy a few 'perpetual calendar' manufacturers.

This possibility falsifies your claim in general, since the Earth's behavior would, for a while at least, be affected by something other than its orbital velocity.
ITYM 'something changing its orbital velocity'. And changes in velocity are permanent, unless something else acts to change it back. Newton, see?

As for whether we "couldn't affect the orbit of Mars", I think you mean that we're highly unlikely to affect it accidentally while actually trying to give it an atmosphere. I agree, but that misses the point.
If you really mean that we aren't capable of ever affect the orbit of a planet like Mars, then you'll need to refute the paper "Astronomical Engineering: A Strategy For Modifying Planetary Orbits". A plausible economic argument might be made against it...
The paper you cite is interesting (got a link to the full version? I don't feel like paying '$33.93 plus tax' for it:), but assumes Mankind to be far more forward-thinking and philanthropic than it currently appears to be :(
Ergo, we can't do it, accidentally or not.

The Earth's average distance from the Sun is governed by it's orbital velocity and nothing else

That's only in the current equilibrium, which is a highly simplified version of the general case. A flyby of a massive body (like Mars) could certainly affect Earth's orbit. This possibility falsifies your claim in general, since the Earth's behavior would, for a while at least, be affected by something other than its orbital velocity.

As for whether we "couldn't affect the orbit of Mars", I think you mean that we're highly unlikely to affect it accidentally while actually trying to give it an atmosphere. I agree, but that misses the point.

If you really mean that we aren't capable of ever affect the orbit of a planet like Mars, then you'll need to refute the paper " Astronomical Engineering: A Strategy For Modifying Planetary Orbits". A plausible economic argument might be made against it...

IANACS (I Am Not A Climate Scientist), but while there are areaa w/ warming trends, there are also some odd cooling trends. Interesting quote from a link below:

Since 1940, however, the Greenland coastal stations data have undergone predominantly a cooling trend. At the summit of the Greenland ice sheet the summer average temperature has decreased at the rate of 2.2 C per decade since the beginning of the measurements in 1987.

Some links:

• Global Warming and the Greenland Ice Sheet
• Reason magazine article mentioning various conflicting evidence / dissenting views on global warming.
• SATELLITES SHOW OVERALL INCREASES IN ANTARCTIC SEA ICE COVER

Fun quote from a actual MIT climatologist, Richard S. Lindzen :

the Antarctic is not warming and there is nothing in the models that distinguish the temperature trends they predict in the Arctic from those in the Antarctic.

My favorite quote from the Reason article:

Climate is messy.