By measuring the tangential and radial velocities of an orbiting body and by knowing the spectral class of its host star, one can utilize this law to determine if that(*) planet lies within the habitable zone.
The Schwarzchild metric for a circular geodesic can be derived by substituting this statement into an expression for the spatial derivative of the metric tensor. By measuring the tangential and radial velocities of an orbiting body and by knowing the spectral class of its host star, one can utilize this law to determine if that(*) planet lies within the habitable zone. One method of deriving this statement involves equating the time derivative of the area to half the specific angular momentum of the small object involved. A factor of 4 times pi-squared over the quantity G times the sum of the involved masses was added to this statement in a correction by Isaac Newton. For 10 points, identify this law of planetary motion which originally stated that the cube orbiting body's semimajor axis is proportional to the period of the orbit squared.
The Schwarzchild metric for a circular geodesic can be derived by substituting this statement into an expression for the spatial derivative of the metric tensor.
Kepler's third law