This page attempts to describe the factors determining a meteor's radiant and the phenomena of radiant drift. The method is illustrated by a calculation for the Persied meteor shower. I'd welcome feedback on the method proposed and would invite you to use the feedback form for this purpose.
The radiant is the point on the celestial sphere from which the trails of meteors appear to radiate. The apparent radiant and the geocentric velocity are both a consequence of both the meteoroid's velocity and the Earth's velocity. If we know the Earths velocity we can derive the meteoroid's heliocentric velocity.
On the 12th August, 2004 the annual Persied meteor shower is predicted to reach its peak of activity between 11:00 and 13:20 UT. At this time the shower is predicted to have a radiant of alpha = 046° and delta +58º. The Persied's geocentric velocity is predicted to be 59 km/s.
At 12:00UT, on the 12th August 2004 the Sun is in the constellation of Leo at an ecliptic longitude is 140º 6' 44.5" and the apex of the Earth's way will be approximately at ecliptic longitude 50º 6' 44.5", in the constellation of Aries. The Earth will be travelling at approximately 29.7847 km/s in the direction of the apex.
At this time the radiant is approximately 40º from the apex of the Earth's way. As we know the Earth's speed and direction and the radiant's location and the meteoroid's geocentric speed, we can determine the meteoroids heliocentric velocity by resolving the meteoroid's velocity into its two components.
This shows that the meteoroids which make up the Persied shower are travelling with a heliocentric velocity of 41.25 km/s and travelling, with respect to the Sun, from a point in Cepheus.
On the 15th July 2004, at the start of the Persied shower, the Sun is in the constellation of Gemini at a ecliptic longitude of 113º 19' 58.6" and consequently the apex is in Pisces at ecliptic longitude 23º 14' 27.6". There is now 72º between the apex of the Earth's way and the direction of the Persied meteoroid's heliocentric velocity.
We can now combine the Earth's velocity and the meteoroid's heliocentric velocity in a vector addition to derive the meteoroid's geocentric velocity. This is now 58km/s and is directed at an angle of 42º from the apex of the Earth's way. This puts the radiant in Cassiopeia.
By the 25th August 2004, at the end of the Persied shower, the Sun is in Leo at an ecliptic longitude of 152º 37' 21.8" and consequently the apex is in Taurus at ecliptic longitude 62º 37' 21.8". There is approximately 66º between the apex of the Earth's way and the direction of the meteoroid's heliocentric velocity. If we repeat the vector addition we find that the meteoroid's geocentric velocity is now 60km/s and is directed at an angle of 39º from the apex of the Earth's way. This puts the radiant in Perius.