Mass (say) 1 kilogram. Then we can measure the mass of any other object in the universe by colliding it with the reference object and measuring the accelerations. Additionally, mass relates a body's momentum p to its linear velocity v: and the body's kinetic energy "K" to its velocity: The primary difficulty with Mach's definition of mass is that it fails to take into account the potential energy (or binding energy) needed to bring two masses sufficiently close to one another to perform the measurement of mass. This is most vividly demonstrated by comparing the mass of the proton in the
Escape velocity "r" from the center of mass of the planet, whose mass is "M". Its initial speed is equal to its escape velocity, formula_6. At its final state, "f", it will be an infinite distance away from the planet, and its speed will be negligibly small and assumed to be 0. Kinetic energy "K" and gravitational potential energy "U" are the only types of energy that we will deal with, so by the conservation of energy, "K" = 0 because final velocity is zero, and "U" = 0 because its final distance is infinity, so where μ is the standard gravitational