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 well-known 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 anti-radiant 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 anti-radiant are on this line. The algorithm for calculating the radiant is as follows:

1. Convert Right Ascension (RA) from hours to degrees.
2. 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
   

3. 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 = rbeg × rend 
   

4. Compute the unit vector for the radiant line. It is perpendicular to the unit vectors found in the previous step.

   rad = n1 × n2 
   

5. If the unit vector for the radiant line points toward the anti-radiant, 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.
6. Convert the coordinates for the unit vector of the radiant into celestial coordinates.

          ________
   ρ   = √ x2 + y2
   RA° = cos-1(x / ρ)    if y < 0 then RA° = 360 - RA°
           _____________
   ρ    = √ x2 + y2 + z2
   Dec° = sin-1(z / ρ)
   

7. Convert RA from degrees to hours.

Copyright © 2004, Stephen R. Schmitt