How do we use Newton's second law of motion and the law of universal gravitation to solve problems that involve the orbital motion of satellites?

Answer: The satellite, if it is orbiting at a certain speed once launched into space, will continue to orbit at that same speed until it collided with some other force, such as debris or something along those lines. In space, with the amount of gravitational pull that surrounds the earth, once something falls into orbit, it will continue to orbit the same way as it began. The earth will continue to pull the satellites towards itself with the same amount of force, and so will keep its orbit consistent.