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Re: three impacts at the K-T boundary



    I'm only a lurker on this list because I have little knowledge of
dinosaurs, but I may know enough physics to shed some light on some of
the issues relating to comet and asteroid impact that have come up on
this thread.

    Let's consider impacts upon the Earth, and discuss the impact
speeds and energies that are dynamically likely: 

    It would be difficult to arrange for a lower impact speed than
that that would result if the object had first somehow been captured
into low Earth orbit -- like a typical artificial satellite.  The
speed on entering the atmosphere would then be the same speed that
such a satellite has on re-entry, about 8 Km/s.

    There's no fundamental physical limit at the high end short of the
speed of light, but there is an astronomically likely limit, imposed
by the likely constraint that the colliding object be gravitationally
bound to the solar system -- that it not be a wanderer, in from
interstellar space.  The greatest speed that such an object can have
as it crosses the Earth's orbit is a little more than 40 Km/s, which
is the required escape velocity from the solar system for an object
that starts its voyage somewhere along the Earth's orbit.
    There's more.  The Earth is not standing still, it is moving in
its orbit at almost 30 Km/s.  If the colliding object happened to be
traveling directly opposite to the Earth's orbital motion at the time
of collision, then its own speed and the Earth's orbital speed would
add, resulting in a relative speed of about 70 Km/s.
    There's still more, for the Earth's gravity is accelerating the
object as it approaches.  To see how much extra speed is obtained, you
square the relative speed without the effect of Earth's gravity, add
in the square of the Earth's 11 Km/s escape velocity, and take the
square root of the result.  For our "bad luck" case of 70 Km/s, this
results in only about another Km/s of speed.

    Thus I think it fair to say that the dynamically likely range of
top-of-the-atmospere impact speeds for a comet or asteroid striking
the Earth is from roughly 8 to roughly 70 Km/s.  The worst case, 70
Km/s, is not likely in any case (just from how things work out if
orbital directions and speeds are distributed randomly).  Furthermore,
speaking very broadly, asteroids tend to have somewhat less weird
orbits than do comets, so a worst-case speed for an asteroid impact is
probably less likely than a worse-case speed for a comet impact.  Were
I to hazard a guess, I would suspect that speeds of 20 to 30 Km/s would
be most common.

    Note that impact energy scales as the square of speed, so the
range of about 9 : 1 in speeds corresponds to a range of about 80 : 1
in energy, for an object of given mass.

    What happened with the recent Jupiter impact was that the comet
was first captured into an orbit -- though not a "low-Jupiter" orbit,
rather one with more energy.  And since Jupiter is much more massive
than Earth, the speeds of its satellites are in any case vastly
greater.  Thus the cometary fragments were moving at something like 50
or 60 Km/s when they hit -- speeds which would be near the high range
of what is likely for impacts upon Earth, but which are hard to avoid
if the target is Jupiter.

                                              --  Jay Freeman