Also worth noting is that some orbital parameters (such as semi-major
axis) are exquisitely sensitive to the value of the initial velocity.
Unless you know that to within a few percent, there's hardly any point
in calculating the parameters at all (although inclination can be a
useful value).
Chris
*******************************
Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com
On 4/14/2014 1:54 PM, Matson, Rob D. wrote:
Hi Chris/Shawn/All,
There is obviously something squirrely going on in that generated orbit.
For one thing, look at the error bars on the velocity -- they cover all
possible velocities (and as Chris points out, impossible velocities as
well).
I do have a comment about the oft-quoted 72 km/sec value. It is derived
from the orbital velocity of the earth around the sun which averages
29.78 km/sec encountering a retrograde body at just below solar system
escape velocity, which is around 42.1 km/sec at the earth's average
distance from the sun. This gets you to 71.88 km/sec. However, earth's
maximum orbital velocity (which occurs at perihelion in early January
each year) is 30.29 km/sec. And solar system escape velocity at earth's
perihelion distance is 42.48 km/sec. So that increases the closing
velocity to 72.77 km/sec. However, this still isn't the theoretical
maximum closing velocity, since I haven't included the acceleration of
the intercepting body due to earth's gravity well.
At an initial closing speed of 72.77 km/sec, there isn't a lot of time
for the earth's gravity to act on the body before it hits the atmosphere,
so the velocity boost is much smaller than earth's escape velocity (11.2
km/sec). From conservation of energy considerations, it can be shown
that the square of the impact velocity is equal to the sum of the
squares of the escape velocity and the approach velocity. So:
Max impact velocity = SQRT(11.2^2 + 72.77^2) = 73.63 km/sec
So in January, it is certainly possible to have a meteor with a
velocity above 73 km/sec. Anything above 73.63 would require the object
to have either originated outside the Solar System, or (as Chris
mentioned) to have been involved in a slingshot encounter with
another planet prior to encountering earth.
--Rob
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