In this problem you will measure the gravitational constant in a series of “observational experiments,” making use of Newton’s law of gravitation and second law of motion as well as Kepler’s third law of planetary motion a)Since measuring the centripetal acceleration of an orbiting body is rather difficult, an alternative approach is to use the body’s rotational period instead. Enter an expression for the gravitational constant, in terms of the distance between Earth and the moon, RME, Earth’s mass,ME, and the moon’s period of rotation around Earth, T. b)Using the expression you entered in part (b) and taking the rotational period of the moon to be T = 27.1 days, what value would Newton have calculated for the gravitation constant, in units of N⋅m2/kg2? Take ME = 5.95×1024 kg and RME = 3.86×108 m. c) Suppose a rocket is launched as described in part (d) with an initial speed of vi = 494 m/s and attains a peak altitude of H = 12.7 km above the surface of Earth. Taking ME = 5.95×1024 kg and Ri = 6.41×106 m, what is the measured value of the gravitational constant, in units of N⋅m2/kg2?
In this problem you will measure the gravitational constant in a series of “observational experiments,” making use of Newton’s law of gravitation and second law of motion as well as Kepler’s third law of planetary motion
a)Since measuring the centripetal acceleration of an orbiting body is rather difficult, an alternative approach is to use the body’s rotational period instead. Enter an expression for the gravitational constant, in terms of the distance between Earth and the moon, RME, Earth’s mass,ME, and the moon’s period of rotation around Earth, T.
b)Using the expression you entered in part (b) and taking the rotational period of the moon to be T = 27.1 days, what value would Newton have calculated for the gravitation constant, in units of N⋅m2/kg2? Take ME = 5.95×1024 kg and RME = 3.86×108 m.
c) Suppose a rocket is launched as described in part (d) with an initial speed of vi = 494 m/s and attains a peak altitude of H = 12.7 km above the surface of Earth. Taking ME = 5.95×1024 kg and Ri = 6.41×106 m, what is the measured value of the gravitational constant, in units of N⋅m2/kg2?
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