Relativistic Momentum

Relativistic Momentum

Classical momentum $p = mv$ is not conserved in all inertial frames. The relativistic fix multiplies by $\gamma$:

$p = \gamma m v = \frac{mv}{\sqrt{1 - v^2/c^2}}$

where $m$ is the rest mass — an invariant property of the particle. At low speeds $\gamma \approx 1$ and we recover $p \approx mv$. As $v \to c$, $p \to \infty$: no finite force can push a massive object to light speed.

Force and Momentum

Newton's second law keeps the same form in relativity: $F = dp/dt$. But since $p = \gamma mv$ and $\gamma$ itself depends on $v$, the force needed to maintain constant acceleration grows without bound as $v \to c$.

Momentum Ratio

The ratio of relativistic to classical momentum is simply $\gamma$:

$\frac{p_\text{rel}}{p_\text{class}} = \gamma$

Your Task

Implement relativistic_momentum(m, v) returning $p = \gamma mv$, and momentum_ratio(v) returning $\gamma$ — the factor by which relativistic momentum exceeds classical momentum. Use $c = 299792458.0$ m/s defined inside each function.