Proper velocity by Hermann Minkowski's flat-space metric equation . Here a reference map frame of yardsticks and synchronized clocks define map position x and map time "t" respectively, and the "d" preceding a coordinate means infinitesimal change. A bit of manipulation allows one to show that proper velocity where as usual coordinate velocity . Thus finite "w" ensures that "v" is less than lightspeed "c". By grouping "γ" with v in the expression for relativistic momentum p, proper velocity also extends the Newtonian form of momentum as mass times velocity to high speeds without a need for relativistic mass. The proper velocity
Earth mass value) in the Schiehallion experiment in the 1770s, and within 1% of the modern value in the Cavendish experiment of 1798. The mass of Earth is estimated to be: which can be expressed in terms of solar mass as: The ratio of Earth mass to lunar mass has been measured to great accuracy. The current best estimate is: The "G" product for the Earth is called the geocentric gravitational constant and equals It is determined using laser ranging data from Earth-orbiting satellites, such as LAGEOS-1. The "G" product can also be calculated by observing the motion of the Moon or