If the speed of the ball at the bottom of the circle is v, what is the expression for the centripetal force on the ball in terms of its speed v and the length L of the string? Take the upward direction as positive and the downward direction as negative when considering the sign of the forces. (Use the following as necessary: m, v and L.)

Without any equipment, you can see stars that are 2{,}800{,}0002,800,0002, comma, 800, comma, 000 light-years away. by looking through a small telescope, you can see stars that are 3{,}112{,}000{,}0003,112,000,0003, comma, 112, comma, 000, comma, 000 light-years away. approximately how many times as far can you see using a small telescope as without any equipment?