Titania, the largest moon of the planet Uranus, has the radius of the earth and the mass of the earth. (a) What is the acceleration due to gravity at the surface of Titania? (b) What is the average density of Titania? (This is less than the density of rock, which is one piece of evidence that Titania is made primarily of ice.)
Solution Step 1 of 6 In the given problem, we need to calculate the acceleration due to gravity on the surface of Titania and average density of titania. Which has radius R = R 1 times of earth radius and T 8 E 1 mass m =T 1700 E times mass of earth. Where Titania is the largest moon of planet Uranus, hence it is under uniform circular motion.(mass of earth(mE) and radius of earth (RE)) Step 2 of 6 Given data, 1 Mass of Titania, m =T 1700 E Using m =E.97× 10 kg 24 m T 1 (5.97 × 10 kg) 1700 20 m T 35.11 × 10 kg Radius of Titania, R = R 1 T 8 E 6 1 6 Using R E6.38× 10 m R T (6838 × 10 m) 3 R T797.5× 10 m To find, Acceleration due to gravity on the surface of Titania, a= Density of titania, = Step 3 of 6 To calculate acceleration due to gravity on the surface of Titania, For circular motion of bodies, the centripetal acceleration is given by 2 a = v R Using v = GM a = GM2 R R Where G is universal gravitational constant, M is mass and R is radius.