Calculating Coil Windings for Bicycle Dynamo LED With 5mm x 10mm Magnet, 323-430 Gs

i'm trying to design a certain type of bicycle dynamo to light an LED on my bike. I'm trying to build something similar to what the company reelight sells: https://www.reelight.com/collections/bike-lights/products/cph?variant=5764959109147It uses a magnet on the bicycle wheel to induce a current in a a coil to drive an LED. Since I want the LED to stay on during the time when no current is induced in the coil I have come up with the design attached. Please correct me if I have made a mistake. I am not an electrical engineer, but I want to learn the basics. I want to calculate the amount of windings necessary to deliver a proper voltage to drive the LED. Also, a large enough power has to be generated when current is induced to drive the LED for the time when no current is induced. Following are all the fixed parameters:- Magnet thickness: 5 mm- Magnet diameter: 10 mm- Distance magnet-coil: 5 mm- Magnetic field strength @5 mm: 323-430 Gs (calculated here: https://www.kjmagnetics.com/calculator.asp?calcType=disc)- LED current: 20 mA- Coil core diameter: 10 mm- Core permeability: ? (unsure)- minimum magnet speed relative to coil: 2 m/sThe orientation of the magnet relative to the coil can be seen in the second attachment. Now i'm trying to figure out how many windings I should use for the coil. For that I tried using the formula for magnetic induction: EMF = -N(dPhi/dt) , but that does not get me anywhere since i'm not sure what to fill in for d Phi and dt. Also, i'm not sure how to proceed from here. What influence does the coil resistance (yet to be determined by wire diameter and windings) have on the current flowing to the capacitor? Could someone help me with this? Thanks so much!

The values should be correct. Have you seen this tool https://www.eeweb.com/tools? Please check if for inductor you find that you want.

Thanks for your answer. It looks like I took the magnetic field in Gauss. It should be Tesla right?  This would change the outcome significantly.

EMF = -N(dPhi/dt) where EMF is in volts. N is number of turns in the coil. Phi is magnetic flux through the coil in teslas*squaremeters. t is time in seconds. dPhi/dt is the rate of change of Phi as t changes, in teslas*squaremeters/seconds. dPhi/dt is the first derivative of Phi with respect to t; see a calculus textbook for details. Phi = B*A where B = magnetic field component perpendicular to coil geometrical area A.
As a starting point, keep the resistance of the coil less than the resistance of the resistor in series with the LED. Papers discussing the design of rectifier circuits discuss this resistance. The ARRL Handbook is one source; there are many others. Look up "capacitor-input filter" for more information.If you don't have an oscilloscope, look into the cheap USB oscilloscopes that work with your computer.

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