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RE: (meteorobs) Radiant rising time

When the Earth encounters a meteoroid, it is on its heliocentric orbit
around the Sun.  However, the Earth's gravity forces it into a hyperbolic
orbit around the Earth.  The curvature introduced into by the Earth's
gravity has the effect of changing its direction to a steeper angle.  With
the meteor overhead (and the center of the Earth beneath you), I hope it
is clear that the curve only acts to raise the radiant's elevation.

Anyway, here is a simple basic program that calculates zenithal
attraction.  Note that the curvature can amount to 90 degrees in extreme
circumstances!  In Porter's "Comets and Meteor Streams", I think he quotes
the maximum as about 19 deg.  This whole section is repeated (without
attribution?) in Lovell's "Meteor Astronomy", including the maximum of
about 19 deg or whatever.

A body with a geocentric velocity of about zero, will be in a near
parabolic orbit about the Earth.  The tangents to a parabola at infinity
are parallel for the incoming and outgoing paths, so when at perigee, it
is moving at 90 deg to the incoming direction.

The program gives a choise of atmospheric velocity (meteoroids actual
velocity including the Earth's gravity) or geocentric velocity (velocity
of collision with the Earth's gravitational attraction removed).

Cheers, Rob

REM ZENITHAL ATTRACTION PROGRAM (RMcN C64 program "ZENITHAL ATTRACT
85/9/5")

CLS
PRINT "ZENITHAL ATTRACTION"

RD = 57.296

PRINT "V[1] = geocentric vel. (km/s)"
PRINT "V[2] = atmospheric vel.(km/s)"
10 PRINT
INPUT "1 or 2"; V
IF V <> 1 AND V <> 2 THEN GOTO 10

20 PRINT

IF V = 1 THEN INPUT ; "V1 "; V1: V2 = SQR(V1 * V1 + 124.9): PRINT : PRINT
USING "V2 = ##.##"; V2
IF V = 2 THEN INPUT ; "V2 "; V2: V1 = SQR(V2 * V2 - 124.9): PRINT : PRINT
USING "V1 = ##.##"; V1

30 PRINT

INPUT "OBSERVED Zenith Distance (deg)"; Z: Z = Z / RD
DZ = 2 * ATN((V2 - V1) / (V2 + V1) * TAN(Z / 2))

PRINT
PRINT USING "DZ = ##.## (deg)"; DZ * RD

PRINT
INPUT "CONTINUE"; C$
IF C$ = "N" OR C$ = "n" THEN END

GOTO 30




Note that word wrap has brought the end of several lines onto another
line.

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