Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Chapter 3, Problem 31E
Suppose astronomers find an earthlike planet that is twice the size of Earth (that is, its radius is twice that of Earth’s). What must be the mass of this planet such that the gravitational force (Fgravity) at the surface would be identical to Earth’s?
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A planet has a mass of M1, a radius of R1, and a density of ρ1. A second planet has a mass of M2, a radius of R2, and a density of ρ2. This problem will explore the relationships between the surface gravities (g1 and g2) of the planets depending on the relative sizes of their masses, radii, and densities.
a) Assume that planet 2 has X times the mass of planet 1, or M2 = XM1. The densities of both planets are the same. Write an expression for the ratio of the surface gravity of planet 2 to planet 1 in terms of X.
b)Suppose now the radius of the second planet is Y times the size of the radius of the first planet, or R2 = YR1. Write an expression for the ratio of the surface gravities, g2/g1 in terms of Y assuming the densities are the same.
c) Suppose now M2 = 8M1 and ρ2 = 8ρ1. What is the ratio of g2/g1 now (here we want the actual number; because you are writing a ratio, the number will be unitless)?
d) Now suppose R2 = 10R1 and ρ2 = 10ρ1. Find the ratio of g2/g1 (again as a number…
Chapter 3 Solutions
Astronomy
Ch. 3 - State Kepler’s three laws in your own words.Ch. 3 - Why did Kepler need Tycho Brahe’s data to...Ch. 3 - Which has more mass: an armful of feathers or an...Ch. 3 - Explain how Kepler was able to find a relationship...Ch. 3 - Write out Newton’s three laws of motion in terms...Ch. 3 - Which major planet has the largest . . . A....Ch. 3 - Why do we say that Neptune was the first planet to...Ch. 3 - Why was Brahe reluctant to provide Kepler with all...Ch. 3 - According to Kepler’s second law, where in a...Ch. 3 - The gas pedal, the brakes, and the steering wheel...
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