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Chapter 12: Problem 20

Where the International Space Station orbits, the gravitational acceleration is just \(11.4 \%\) less than its value on the surface of the Earth. Nevertheless, astronauts in the space station float. Why is this so?

Short Answer

Expert verified
Answer: Astronauts float inside the ISS because they are in a state of free fall, experiencing the same gravitational acceleration as the space station itself. This causes them to float and feel weightless relative to their environment, even though the gravitational acceleration in the ISS orbit is slightly less than on Earth's surface (8.68 m/s² compared with 9.81 m/s²).

Step by step solution

01

Review the concept of gravitational acceleration

Gravitational acceleration is the acceleration of an object due to the force of gravity. On Earth, the gravitational acceleration (often represented as g) is approximately 9.81 m/s². The value of gravitational acceleration varies depending on where an object is in relation to Earth, such as greater distance leading to a lower acceleration.
02

Define free fall

Free fall is a state in which an object experiences only gravity's pull and no other forces. In this state, all objects fall at the same rate, regardless of their mass. When an object is in free fall, people inside it will float as they are subject to the same acceleration, making them weightless relative to the object. Astronauts in the ISS experience free fall, which makes them float.
03

Calculate the gravitational acceleration on the surface of Earth

The gravitational acceleration on Earth's surface is known as a standard value, approximately: g = 9.81 m/s²
04

Calculate the gravitational acceleration in the ISS orbit

The gravitational acceleration in the ISS orbit is given as 11.4% less than on Earth. Therefore, we can calculate the gravitational acceleration in the ISS orbit (g_iss) using the following equation: g_iss = g - 0.114 * g = 0.886 * g Now, substitute the value of g: g_iss = 0.886 * 9.81 m/s² g_iss ≈ 8.68 m/s²
05

Explain why astronauts float in the ISS

As calculated previously, the gravitational acceleration in the ISS orbit is slightly less than on Earth's surface (8.68 m/s² compared with 9.81 m/s²). Although there is gravitational acceleration present, the ISS and its astronauts are continuously falling towards Earth in a circular path - they are experiencing a free fall. In this state of free fall, astronauts on the ISS feel weightless relative to their environment because they are subject to the same gravitational acceleration as the ISS itself. This ensures that they float inside the space station despite the presence of gravity.

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Most popular questions from this chapter

Two identical 20.0 -kg spheres of radius \(10 \mathrm{~cm}\) are \(30.0 \mathrm{~cm}\) apart (center-to-center distance). a) If they are released from rest and allowed to fall toward one another, what is their speed when they first make contact? b) If the spheres are initially at rest and just touching, how much energy is required to separate them to \(1.00 \mathrm{~m}\) apart? Assume that the only force acting on each mass is the gravitational force due to the other mass.

A satellite is in a circular orbit around a planet. The ratio of the satellite's kinetic energy to its gravitational potential energy, \(K / U_{\mathrm{g}}\), is a constant whose value is independent of the masses of the satellite and planet, and of the radius and velocity of the orbit. Find the value of this constant. (Potential energy is taken to be zero at infinite separation.)

With the usual assumption that the gravitational potential energy goes to zero at infinite distance, the gravitational potential energy due to the Earth at the center of Earth is a) positive. b) negative. c) zero. d) undetermined.

What is the magnitude of the free-fall acceleration of a ball (mass \(m\) ) due to the Earth's gravity at an altitude of \(2 R\), where \(R\) is the radius of the Earth?

A planet is in a circular orbit about a remote star, far from any other object in the universe. Which of the following statements is true? a) There is only one force acting on the planet. b) There are two forces acting on the planet and their resultant is zero. c) There are two forces acting on the planet and their resultant is not zero. d) None of the above statements are true.
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