Chapter 12, Problem 60PCE

The magnitude of the tidal force between the International Space Station (ISS) and a nearby astronaut on a spacewalk is approximately 2GmMa/r³. In this expression, M is the mass of the Earth, r = 6.79 × 10⁶ m is the distance from the center of the Earth to the orbit of the ISS, m = 125 kg is the mass of the astronaut, and a = 10 m 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 10 m apart and the ISS has a mass of 420,000 kg. (c) Is the ISS orbit inside or outside the Roche limit?