Proper velocity Proper velocity In relativity, proper velocity, also known as celerity, is an alternative to velocity for measuring motion. Whereas velocity relative to an observer is distance per unit time where both distance and time are measured by the observer, proper velocity relative to an observer divides observer-measured distance by the time elapsed on the clocks of the traveling object. Proper velocity equals velocity at low speeds. Proper velocity at high speeds, moreover, retains many of the properties that velocity loses in relativity compared with Newtonian theory. For example, proper velocity equals momentum per unit mass at any speed, and therefore
Mass ratio from Tsiolkovsky's rocket equation: where This equation can be rewritten in the following equivalent form: The fraction on the left-hand side of this equation is the rocket's mass ratio by definition. This equation indicates that a Δv of formula_4 times the exhaust velocity requires a mass ratio of formula_5. For instance, for a vehicle to achieve a formula_6 of 2.5 times its exhaust velocity would require a mass ratio of formula_7 (approximately 12.2). One could say that a "velocity ratio" of formula_4 requires a mass ratio of formula_5. Sutton defines the mass ratio inversely as: In this case, the values