time dilation t' = t/γ mass increase m' = mγ length shortening L' = L/γ γ = 1/√(1–(V²/c²)) relativistic momentum is γmv relativistic total energy is: E = mc²γ Relativistic KE = mc²γ–mc² = mc²(γ–1) γ = 1/√(1–(V²/c²)) relativistic speed addition S = (v+u)/(1+vu/c²) γ = 1/√(1–(V²/c²)) γ = 1 + (V²/2c²) for small v Speed of light c = 299,792,458 metres per second or 86,282 miles per second Momentum P = γmV γ = 1/√(1–V²/c²) m is rest mass V = speed Gamma values at v = 1 m/s, γ = 1 + 5.6e-18 at v = 3 m/s, γ = 1 + 5.6e-17 at v = 10 m/s, γ = 1 + 5.6e-16 at v = 30 m/s, γ = 1 + 5.6e-15 at v = 100 m/s, γ = 1 + 5.6e-14 at v = 300 m/s, γ = 1 + 5.6e-13 at v = 1000 m/s, γ = 1 + 5.6e-12 at v = 3000 m/s, γ = 1 + 5.6e-11 at v = 10000 m/s, γ = 1 + 5.6e-10 at 0.0001c, 3e4 m/s, γ = 1.0000000056 at 0.0003c, 1e5 m/s, γ = 1.000000056 at 0.001c, 3e5 m/s, γ = 1.00000056 at 0.003c, 1e6 m/s, γ = 1.0000056 at 0.01c, 3e6 m/s, γ = 1.000056 at 0.03c, 1e7 m/s, γ = 1.00056 at 0.1c, 3e7 m/s, γ = 1.0050 at 0.2c, 6e7 m/s, γ = 1.0206 at 0.3c, 9e7 m/s, γ = 1.048 at 0.4c, 1.2e8 m/s, γ = 1.081 at 0.5c, 1.5e8 m/s, γ = 1.15 at 0.6c, 1.8e8 m/s, γ = 1.25 at 0.7c, 2.1e8 m/s, γ = 1.40 at 0.75c, 2.24e8 m/s, γ = 1.51 at 0.8c, 2.4e8 m/s, γ = 1.67 at 0.866c, 2.6e8 m/s, γ = 2 at 0.9c, 2.7e8 m/s, γ = 2.29 at 0.98c, 2.94e8 m/s, γ = 5.05 at 0.99c, 2.97e8 m/s, γ = 7.09 at 0.999c, γ = 22.4 at 0.9995c, γ = 31.6 at 0.9999c, γ = 70.7 at 0.99995c, γ = 100 at 0.9999995c, γ = 1000 at 0.999999995c, γ = 10000 |
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