coordinates for the metric (e.g. a local Lorentz tetrad like that which global positioning systems provide information on) to describe time in seconds, and space in distance units along perpendicular axes. If we multiply the above equation by the traveling object's rest mass m, and divide by Lorentz factor γ = dt/dτ, the spacelike components express the rate of momentum change for that object from the perspective of the coordinates used to describe the metric. This in turn can be broken down into parts due to proper and geometric components of acceleration and force. If we further multiply the time-like component by lightspeed c, and define coordinate velocity as , we get an expression for rate of energy change as well: (timelike) and (spacelike). Here ao is an acceleration due to proper forces and ag is, by default, a geometric acceleration that we see applied to the object because of our coordinate system choice. At low speeds these accelerations combine to generate a coordinate acceleration like , while for unidirectional motion at any speed ao's magnitude is that of proper acceleration α as in the section above where α = γ3a when ag is zero. In general expressing these accelerations and forces can be complicated. Nonetheless if we use this breakdown to describe the connection coefficient (Γ) term above in terms of geometric forces, then the motion of objects from the point of view of any coordinate system (at least at low speeds) can be seen as locally Newtonian. This is already common practice e.g. with centrifugal force and gravity. Thus the equivalence principle extends the local usefulness of Newton's laws to accelerated coordinate systems and beyond. Surface dwellers on a planet For low speed observers being held at fixed radius from the center of a spherical planet or star, coordinate acceleration ashell is approximately related to proper acceleration ao by: where the planet or star's Schwarzschild radius . As our shell observer's radius approaches the Schwarzschild radius, the proper acceleration ao needed to keep it from falling in becomes intolerable. On the other hand, for , an upward proper force of only is needed to prevent one from accelerating downward. At the Earth's surface this becomes: where is the downward 9.8 m/s2 acceleration due to gravity, and is a unit vector in the radially outward direction from the center of the gravitating body. Thus here an outward proper force