Mechanical energy mechanical energy of the colliding objects has been converted into an equal amount of heat. Thus, the total energy of the system remains unchanged though the mechanical energy of the system has reduced. A satellite of mass formula_4 at a distance formula_5 from the centre of Earth possesses both kinetic energy, formula_6, (by virtue of its motion) and gravitational potential energy, formula_7, (by virtue of its position within the Earth’s gravitational field; Earth's mass is formula_8). Hence, mechanical energy formula_9 of a satellite is given by If the satellite is in circular orbit, the energy conservation equation can be further
Biproduct If the product formula_9 and coproduct formula_10 both exist for some pair of objects "A", then there is a unique morphism formula_11 such that It follows that the biproduct formula_15 exists if and only if "f" is an isomorphism. If C is a preadditive category, then every finite product is a biproduct, and every finite coproduct is a biproduct. For example, if formula_9 exists, then there are unique morphisms formula_17 such that To see that formula_9 is now also a coproduct, and hence a biproduct, suppose we have morphisms formula_22 for some object formula_23. Define formula_24 Then formula_25 is a