**GeoMagSphere Web Calculators**

GeoMagSphere data sets and results can be freely downloaded or copied. However, the user should make the appropriate acknowledgment or citation, e.g., see Citations or Bibliography pages. The data generated by using the Calculator may be used by GeoMagSphere developers for statistical purpose.

**Time Length Calculator**

This page enables users to calculate, for different particles as electrons and ions, starting fron the Rigidity to the Kinetic Energy per Nucleons, the possible trajectory time and and trajectory length

This two quantities are obtained from the relativistic particle's \(\gamma\) that provide the particle's velocity:

\begin{equation}

\gamma = \sqrt{\frac{(T+T_{0})^{2}}{T_{0}^{2}}}

\end{equation}

\begin{equation}

v = c\cdot \sqrt{1-\frac{1}{\gamma^{2}}}

\end{equation}

The relation between Rigidity and Kinetic Energy per Nucleon is:

\begin{equation}

R=\frac{A}{Z}\cdot\sqrt{T^{2}+2TT_{0}}

\end{equation}

Where \(R\) is the Rigidity, \(A\) is the mass number, \(Z\) is the charge, \(T\) is the kinetic energy per nucelon, \(T_{0}\) is the rest energy per nucelon.

To run the code follow this link:

## Input Parameters

Input data are:

- Particle (0 for Electrons, 1 for Protons, 2 for Helium nuclei, etc., up to 26 for iron)
- Input type: 0 for Rigidiy or 1 for Energy/Nucleon
- Rigidity (or Energy/Nucleon) value in GV (GeV)

## Output Parameters

Output data are:

- Particle Beta
- Particle Velocity
- Trajectory Length for 1,5,10 sec
- Trajectory Time for 1,10,100 \(R_{0}\)

## Info

For any additional informations or questions you can ask