[meteorite-list] Venusian Meteorites (Again) and Mercury Too!

From: Sterling K. Webb <kelly_at_meteoritecentral.com>
Date: Thu Apr 22 10:28:35 2004
Message-ID: <3F98B604.A809F4A1_at_bhil.com>

Hi,

    Another interesting aspect of getting Venus rocks to land on Earth
is the orbit (or orbits) required to do it.
    Since Venus orbits closer to the Sun than the Earth, its orbital
velocity (35,000 m/sec) is greater than the Earth's (29,800 m/sec).
While there are a large variety of orbits which might allow a Venus rock
to whack the Earth, the orbit most likely to deliver Venus rocks to the
Earth is the minimum energy one. That's a cotangential elipse (called a
Hohmann orbit after Dr. Hohmann who wrote the book on interplanetary
flight back in 1925). It's an elipse that just touches the orbit of
Venus at its closest to the Sun and just touches or barely passes the
orbit of the Earth at its furthest.
    Once we've knocked that rock off Venus, it's moving at the Venus
orbital speed (35,000 m/sec). To swing out further into the solar system
to get as far as to Earth, it needs to be speeded up to 37,700 m/sec.
Which is another way of saying that the only Venus rocks to reach the
Earth have to leave Venus FASTER than the Venusian escape velocity, with
a residual velocity of 2700 m/sec pointed in more or less the right
direction.
    Ho Hum, you say. Well, here's the interesting point. When that rock
arrives at the Earth, it will be moving SLOWER than the Earth in its
orbit by 2500 m/sec. If it happens to swing up into the Earth's orbital
path just ahead of the Earth, the Earth will run it down and smack right
into it! And if it happens to swing up into the Earth's orbital path
just behind the Earth, the Earth will be running away from it. Of
course, the Earth's gravity will grab the trailing object and accelerate
it down to the planet, BUT it will arrive with less than the Earth's
escape velocity.
    That is highly unusual. If an object is standing still with respect
to the Earth, it will land at escape velocity (ignoring that pesky
atmosphere for a moment). If an object is moving toward the Earth, it
will land at a speed greater than escape velocity, in many cases, MUCH
greater than escape velocity (up to 72,300 m/sec for the fastest
possible solar system object).
    For an object approaching on an interior orbit (like from Venus) it
has in effect a negative approach velocity, making it possible for it to
fall in at a speed no greater than 9200 m/sec. The SLOWER an object
enters the atmosphere, the greater are its chances of surviving to
become a meteorite in the hand. Entry speed is, in fact, the largest
single factor determining survival.
    And what is true for Venus rocks is even more true for Mercury
rocks. They can arrive at the Earth moving even more slowly and landing
at an even lower speed. So, paradoxically, Earth-arriving meteorites
originating from Venus and Mercury can be more favored for survival
through the atmosphere than any other incoming object, like the
conventional Asteroid Belt objects.
    And while I described the simplest direct orbit transfer from Venus
to the Earth, any object that leaves Venus with an excess velocity of
2700 m/sec or greater, heading in any direction, will always cross the
Earth's orbital sphere and, after perturbations from the solar plane,
eventually cross the Earth's orbital plane and finally, sooner or later,
it will do so when the Earth is there -- splat! In other words, if it
doesn't hit anything else, it'll get here! Ditto for the Mercury rock.
What's a hundred million years to a rock?
    So, where are those dozens and dozens of Venus meteorites?


Sterling K. Webb
Received on Fri 24 Oct 2003 01:17:57 AM PDT