Log out Go to App
Go to App

Learning Materials

Features

Discover

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Compare the magnitudes of the gravitational force that the Earth exerts on the Moon and the gravitational force that the Moon exerts on the Earth. Which is larger?

An asteroid is discovered to have a tiny moon that orbits it in a circular path at a distance of \(100 . \mathrm{km}\) and with a period of \(40.0 \mathrm{~h}\). The asteroid is roughly spherical (unusual for such a small body) with a radius of \(20.0 \mathrm{~km} .\) a) Find the acceleration of gravity at the surface of the asteroid. b) Find the escape velocity from the asteroid.

The weight of a star is usually balanced by two forces: the gravitational force, acting inward, and the force created by nuclear reactions, acting outward. Over a long period of time, the force due to nuclear reactions gets weaker, causing the gravitational collapse of the star and crushing atoms out of existence. Under such extreme conditions, protons and electrons are squeezed to form neutrons, giving birth to a neutron star. Neutron stars are massively heavy-a teaspoon of the substance of a neutron star would weigh 100 million metric tons on the Earth. a) Consider a neutron star whose mass is twice the mass of the Sun and whose radius is \(10.0 \mathrm{~km} .\) If it rotates with a period of \(1.00 \mathrm{~s}\), what is the speed of a point on the Equator of this star? Compare this speed with the speed of a point on the Earth's Equator. b) What is the value of \(g\) at the surface of this star? c) Compare the weight of a 1.00 -kg mass on the Earth with its weight on the neutron star. d) If a satellite is to circle \(10.0 \mathrm{~km}\) above the surface of such a neutron star, how many revolutions per minute will it make? e) What is the radius of the geostationary orbit for this neutron star?

Halley's comet orbits the Sun with a period of 76.2 yr. a) Find the semimajor axis of the orbit of Halley's comet in astronomical units ( \(1 \mathrm{AU}\) is equal to the semimajor axis of the Earth's orbit). b) If Halley's comet is \(0.56 \mathrm{AU}\) from the Sun at perihelion, what is its maximum distance from the Sun, and what is the eccentricity of its orbit?

A man inside a sturdy box is fired out of a cannon. Which of following statements regarding the weightless sensation for the man is correct? a) The man senses weightlessness only when he and the box are traveling upward. b) The man senses weightlessness only when he and the box are traveling downward. c) The man senses weightlessness when he and the box are traveling both upward and downward. d) The man does not sense weightlessness at any time of the flight.
See all solutions

Recommended explanations on Physics Textbooks

Fundamentals of Physics

Read Explanation

Magnetism

Read Explanation

Translational Dynamics

Read Explanation

Medical Physics

Read Explanation

Turning Points in Physics

Read Explanation

Measurements

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free