The following information applies to the next three questions (34 through 36). I

Question

The following information applies to the next three questions (34 through 36). In 2014 the Rosetta spacecraft landed a robotic probe (the Philae) on the comet Churyumov-Gerasimenko (called 67P for short). This was the first ever soft landing of a probe on a comet. In this series of questions, we will take the shape of comet 67P to be a sphere with a radius of the 2000 meters, and having a mass of 1.00 Times 10^13 kg. If the Rosetta spacecraft is in a circular orbit at a distance of 10.0 km from the center of the comet, then what is the orbital speed of the Rosetta about the comet? 0.258 m/s 4.67 m/s 8.17 m/s 66.7 m/s What is the acceleration due to gravity at the surface of comet 67P? zero 1.67 Times 10^-4 m/s^2 0.167 m/s^2 0.334 m/s^2 9.80 m/s^2 The robotic probe, Philae, when placed on a spring scale on the surface of the earth weighed 980 newtons. What would the Philae weigh on the surface of comet 67P? zero 1.67 Times 10^-2 N 16.7 N 33.4 N 980 N

Explanation / Answer

34. for circular motion,

grvitational force = centripetal force

G M m / d^2 = m v^2 / d

G M / d = v^2

v^2 = (6.67 x 10^-11 x 1 x 10^13 ) / (10 x 10^3)

v = 0.258 m/s

Ans(a)

35. acceleration due to gravity at surface, g' = G M / R^2

= (6.67 x 10^-11 x 1 x 10^13) / (2000)^2

= 1.67 x 10^-4 m/s^2

ANs(B)_

36.
on earth, W = mg

on comet : W' = m g'

W' / W = m g' / m g

W ' / W = g' / g

W' / 980 = (1.67 x 10^-4) / 9.8

W' = 1.67 x 10^-2 N

Ans(B)

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