Relativistic Energy

Relativistic Energy

Einstein's most famous equation gives the rest energy of a particle:

$E_0 = mc^2$

This is the energy locked in a particle's mass — even at complete rest. The total relativistic energy includes the kinetic contribution via the Lorentz factor $\gamma$:

$E = \gamma mc^2$

The kinetic energy is the difference between total and rest energy:

$K = E - E_0 = (\gamma - 1)mc^2$

Classical Limit

When $v \ll c$, the Taylor expansion of $\gamma$ gives:

$K \approx \frac{1}{2}mv^2$

This recovers the Newtonian result, confirming relativity reduces to classical mechanics at low speeds.

Your Task

Implement:

• rest_energy(m) — returns $E_0 = mc^2$
• total_energy(m, v) — returns $E = \gamma mc^2$
• kinetic_energy(m, v) — returns $K = (\gamma - 1)mc^2$

Use $c = 299792458.0$ m/s defined inside each function.