LVL 2 8. In each case, rearrange the equation to solve for the variable in question, then determine the factor by which the identified variable will change using the derived equation. Situation Derived equation Factor of change for the variable in question The radius of an object's circular path changes by a factor of 8 while the speed changes by a factor of 4. By what factor must the period change? 2TR The mass of a planet changes by a factor of 1/s. By what factor must its radius change in order for an object on its surface to experience the same gravitational field? The mass of both objects changes by a factor of 1/s and 5. By what factor must the distance between the two objects centers change in order for the force of gravity to remain constant? F =6- The mass of an object in orbit changes by a factor of 6 while the radius of its orbital path changes by a factor of 2. By what factor must the speed change in order for the object to maintain the same centripetal acceleration? LVL 3 9. A brass ball with mass m is transported to the Moon. (The radius of the Moon is R and its mass is M) a. Derive an equation for the acceleration due to gravity on the Moon. b. Compare the mass of the brass ball on Earth to its mass on the Moon. c. Derive an equation for the weight of the brass ball on the moon. d. If this brass ball were dropped from a height of H above the surface of the moon, derive an equation for he long it will take for the object to reach the ground