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A science-fiction tale describes an artificial “planet” in the form of a band completely
Chapter 5, Problem 65P(choose chapter or problem)
(III) A science-fiction tale describes an artificial "planet" in the form of a band completely encircling a sun (Fig. ). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of
as on Earth. What will be the period of revolution, this planet's year, in Earth days?
FIGURE 5-40 Problem 65
Questions & Answers
QUESTION:
(III) A science-fiction tale describes an artificial "planet" in the form of a band completely encircling a sun (Fig. ). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of
as on Earth. What will be the period of revolution, this planet's year, in Earth days?
FIGURE 5-40 Problem 65
ANSWER:
Solution 65P
Step 1 of 4:
Consider an artificial planet is made as a circular ring with the same gravity that of Earth and the same distance from the Sun. The gravity of the planet is provided as it rotates quickly. We are going to find the period of revolution of the artificial planet in the year.
The normal force providing the equivalent gravity is given by
Where m is the mass of the planet
g is acceleration due to gravity (equivalent to 9.8 m/s2)
This normal force acts towards the center of the Sun.