Please all? Problem 2: In this problem you will measure the gravitational constant in a series of "observational experiments," making use of Newton's law ofgravitation and second law of motion as well as Kepler's third law of planetary motion. Part (a) Newton measured the centripetal acceleration of the moon in its orbit around Earth by comparing the force Earth exerts on the moon withthe force Earth exerts on an apple. He obtained a value of a, = 2.73×10-3 m/s?. If Newton had taken the mass of Earth to be Mp = 5.99×1024 kg and the meandistance between the centers of Earth and the moon to be RME = 3.83×10 m, what value would he have obtained for the gravitational constant, in units ofN-m?/kg?; Part (b) Since measuring the centripetal acceleration of an orbiting body is rather difficult, an alternative approach is to use the body's rotationalperiod instead. Enter an expression for the gravitational constant, in terms of the distance between Earth and the moon, RVF, Earth's mass,Mp, and the moon'speriod of rotation around Earth, T.Part (c) Using the expression you entered in part (b) and taking the rotational period of the moon to be T= 27.4 days, what value would Newtonhave calculated for the gravitation constant, in units of N-m2/kg? Take Mp = 5.99×1024 kg and RVE = 3.83×10° m.Part (d) The gravitational constant may also be calculated by analyzing the motion of a rocket. Suppose a rocket is launched vertically from thesurface or Earth at an initial speed of v;. Its initial distance from the center of Earth is R;, the radius of Earth. Its peak distance, where its speed is momentarilyzero is, is Rç. For simplicity, ignore air resistance and Earth's rotation. Enter an expression for the gravitational constant, in terms of v;, R;. Rf and Mg.• Part (e) Suppose a rocket is launched as described in part (d) with an initial speed of v; = 508 m/s and attains a peak altitude of H=12.4 km abovethe surface of Earth. Taking ME = 5.99×1024 kg and R; = 6.39×10° m, what is the measured value of the gravitational constant, in units of N-m2/kg??

Name: Please all? Problem 2: In this problem you will measure the gravitatio
Uploaded: 2024-03-20T06:56:46.000Z
Channel: Bartleby
Description: Please all? Problem 2: In this problem you will measure the gravitational constant in a series of "observational experiments," making use of Newton's law ofgravitation and second law of motion as well as Kepler's third law of planetary motion. Part (