natural units, particularly geometrized unit systems, such as Planck units and Stoney units. When expressed in terms of such units, the value of the gravitational constant will generally have a numeric value of 1 or a value close to it. Due to the significant uncertainty in the measured value of G in terms of other known fundamental constants, a similar level of uncertainty will show up in the value of many quantities when expressed in such a unit system. Orbital mechanics In astrophysics, it is convenient to measure distances in parsecs (pc), velocities in kilometres per second (km/s) and masses in solar units . In these units, the gravitational constant is: For situations where tides are important, the relevant length scales are solar radii rather than parsecs. In these units, the gravitational constant is: In orbital mechanics, the period of an object in circular orbit around a spherical object obeys where is the volume inside the radius of the orbit. It follows that This way of expressing shows the relationship between the average density of a planet and the period of a satellite orbiting just above its surface. For elliptical orbits, applying Kepler's 3rd law, expressed in units characteristic of Earth's orbit: where distance is measured in terms of the semi-major axis of Earth's orbit (the astronomical unit, AU), time in years, and mass in the total mass of the orbiting system (). The above equation is exact only within the approximation of the Earth's orbit around the Sun as a two-body problem in Newtonian mechanics, the measured quantities contain corrections from the perturbations from other bodies in the solar system and from general relativity. From 1964 until 2012, however, it was used as the definition of the astronomical unit and thus held by definition: Since 2012, the AU is defined as exactly, and the equation can no longer be taken as holding precisely. The quantity —the product of the gravitational constant and the mass of a given astronomical body such as the Sun or Earth—is known as the standard gravitational parameter (also denoted ). The standard gravitational parameter appears as above in Newton's law of universal gravitation, as well as in formulas for the deflection of light caused by gravitational lensing, in Kepler's laws of planetary motion, and in the formula for escape velocity. This quantity gives a convenient simplification of various gravity-related formulas. The product is known much