The magnitude of the tidal force between the International Space Station (ISS) a
ID: 1997524 • Letter: T
Question
The magnitude of the tidal force between the International Space Station (ISS) and a nearby astronaut on a spacewalk is approximately 2GmMa/r^3 . In this expression, M is the mass of the Earth, r=6.79×10^6m is the distance from the center of the Earth to the orbit of the ISS, m=135kg is the mass of the astronaut, and a=19m is the distance from the astronaut to the center of mass of the ISS.
a.)Calculate the magnitude of the tidal force for this astronaut. This force tends to separate the astronaut from the ISS if the astronaut is located along the line that connects the center of the Earth with the center of mass of the ISS.
b.)Calculate the force of gravitational attraction between the astronaut and the ISS if they are 19 m apart and the ISS has a mass of 420,000 kg.
Explanation / Answer
(A) F = 2 G m Ma / r^3
F = (2 x 6.67 x 10^-11) (135) (5.972 x 10^24) / (6.79 x 10^6)^3
F = 3.44 x 10^-4 N
(B) Fg = G M m / r^2
Fg = (6.67 x 10^-11) (420 000)(135) / (19^2)
= 1.05 x 10^-5 N
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