{units} are provided for information only
The following relationships apply to any and all consistent units, both metric and Imperial
The symbol ᶜ refers to radians
Momentum (p) = m.a.t = m.v {kg.m/s}
Force (F) = m.a {kg.m/s²}
Energy (U) = F.d = m.a.d {kg.m/s² . m}
Potential Energy (Uᴾ) = m.a.d {kg.m²/s²}
Kinetic Energy (Uᴷ) = ½.m.v² {kg.m²/s²}
Deformation Energy (Uᴰ) = ½.m.a.y {kg.m/s² . m}
Work (W) = Energy {kg.m²/s²}
Power (P) = m.a.d / t {kg.m/s² . m / s}
Energy = Work = Power . t = Momentum . v
Where:
m = mass {kg}
a = acceleration {m/s²}
d = distance {m}
y = deformation {m}
v = velocity {m/s}
t = time {s}
Inertia (I) = ⅖.m.R² {kg.m²}
Torque (T) = m.α.R² {kg . ᶜ/s² . m²}
Energy = ½.I.ω² = ½ . ⅖.m.R² . ω² = ½ .⅖ . m.(ω.R)² [= ⅕.m.v²] {kg . ᶜ²/s² . m²}
Work = 2π.T {ᶜ . kg.m²/s²}
Power = 2π.N.T = ω.T {ᶜ/s . kg.m²/s²}
Energy = 2π . Work = 2π.t . Power = (2π)² . Torque
Where:
m = mass {kg}
α = angular acceleration (ᶜ/s²)
R = radius {m}
v = rotational velocity at the surface of the mass {m/s}
ω = angular velocity {ᶜ/s}
t = time {s}
2π.t = angular period {ᶜ.s}
Power is defined as energy disipated over a period of time (Joules per second).
Whilst a satellite's total energy remains constant throughout its orbit, both potential and kinetic energies vary.
A satellite's orbital power can be defined as the difference between the ...
... potential (gravitational) energy of a satellite at its perigee and that at its apogee divided by the time taken to travel between the two points;
Pᴾ = (PEₚ-PEₐ) / (tₒ/2)
... or the kinetic energy of a satellite at its perigee and that at its apogee divided by the time taken to travel between the two points;
Pᴷ = (KEₚ-KEₐ) / (tₒ/2)
where tₒ is the orbital period
Both of which will be equal; Pᴾ = Pᴷ
You will find further reading on this subject in reference publications(1, 2, 3 & 4)