Notes
What
is the radiant of a meteor shower?
Small
bits of rock escape from comets when they are warmed by the Sun.
This debris spreads out but tends to remain in the comets orbit.
Meteor showers occur when the Earth crosses the orbit of a comet
in the path of the comet debris. During a meteor shower, the meteors
appear to come from a point in the sky called the radiant. This
effect is an optical illusion. The comet debris that produces the
shower is moving in parallel trajectories; because parallel lines
appear to meet at infinity, the meteors seem to radiate from a point.
For
wellknown meteor showers, the coordinates for the radiant position
are usually given at the peak of the shower. However, a radiant
position will drift slowly across the sky due to the Earth's orbital
motion around the Sun.
Computing
the radiant of a meteor shower
As
seen from a point on the Earth's surface, meteor trails will appear
to be following great circle paths. The great circles for meteors
of a shower have two common intersection points; the radiant above
the horizon and the antiradiant below. The geometric definition
of a great circle is the intersection of the sphere and a plane
that passes through the center of the sphere. We can make use of
this fact together with observation of the right ascension and declination
of the beginning and ending points of meteor trails to compute the
location of a radiant from two trails.
Three
points can define a plane. The beginning and ending points of a
meteor trail and the center of the Earth define a plane that passes
through the celestial sphere that gives us the great circle for
the meteor trail. A second set of three points defines another plane
for the great circle of a second meteor trail. The intersection
of the two planes is a straight line. The radiant and antiradiant
are on this line. The algorithm for calculating the radiant is as
follows:
 Convert
Right Ascension (RA) from hours to degrees.
 Convert
the coordinates of the beginning and ending points of meteor trail
into Cartesian coordinates using:
x = sin(90  Dec°)·cos(RA°)
y = sin(90  Dec°)·sin(RA°)
z = cos(90  Dec°)
r = {x, y, z} as a unit vector from the center of the earth
 Compute
the unit vectors perpendicular to the planes of the meteor trails
by calculating vector cross product of two vectors in the plane,
namely, the vectors from the Earth's center to the points defining
the meteor trail.
n = r_{beg} × r_{end}
 Compute
the unit vector for the radiant line. It is perpendicular to the
unit vectors found in the previous step.
rad = n_{1} × n_{2}
 If
the unit vector for the radiant line points toward the antiradiant,
change the sign of each element. One way to do this is to calculate
the average distance to the beginning of the meteor trails for
unit vector and its negative. The shorter average corresponds
to the correct direction.
 Convert
the coordinates for the unit vector of the radiant into celestial
coordinates.
________
ρ = √ x^{2} + y^{2}
RA° = cos^{1}(x / ρ) if y < 0 then RA° = 360  RA°
_____________
ρ = √ x^{2} + y^{2} + z^{2}
Dec° = sin^{1}(z / ρ)
 Convert
RA from degrees to hours.
Copyright © 2004, Stephen R. Schmitt
