Relativistic Motion

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