Consider a satellite that is in a circular orbit around the Earth. The speed of the satellite decreases. What will happen to the satellite's orbital radius and period of revolution? Please justify your answer using principles of physics.

As the speed of the satellite decre ases , its orb ital radius will increase and its period of revolution will decrease . This is because the orb ital velocity of the satellite is directly proportional to the square root of its orb ital radius , according to Ke pler ' s third law of planet ary motion . \n \n The equation for Ke pler ' s third law is : T ^ 2 = 4 π ^ 2 a ^ 3 / G , where T is the period of revolution of the satellite , a is its orb ital radius , and G is the gravit ational constant . \n \n If the speed of the satellite decre ases , then its orb ital radius will increase because the satellite will take more time to complete one orbit around the Earth . This is because the time it takes to complete an orbit is in vers ely proportional to the square root of the orb ital radius , according to Ke pler ' s third law . \n \n There fore , as the speed of the satellite decre ases , its orb ital radius will increase , and its period of revolution will decrease . This is a basic principle of physics that describes the motion of objects in or bits around a central body , such as the Earth . </s>