Astronomers think that Mercury's scarps could have formed if...

Name: Problem 1, Chapter 38: Pathways to Astronomy
Uploaded: 2020-06-11T22:16:25-08:00
Duration: 1 min 17 s
Channel: Mayukh Banik
Description: Astronomers think that Mercury's scarps could have formed if the circumference of the planet shrunk by about 3 kilometers. By what percentage would Mercury's 2439 -km radius have to have changed in order to produce this reduction in circumference? What percentage decrease in Mercury's volume is this?

Astronomers think that Mercury's scarps could have formed if the circumference of the planet shrunk by about 3 kilometers. By what percentage would Mercury's 2439 -km radius have to have changed in order to produce this reduction in circumference? What percentage decrease in Mercury's volume is this?

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Key Concepts

Percentage Change Calculations

Percent change calculations involve finding the ratio of the change in a quantity to its original value, and then expressing this ratio as a percentage. This process is vital for comparing how small alterations in measurements, such as radius or volume, can affect the overall structure or behavior of an object in a relative sense. It provides a normalized way to understand differences across significantly different magnitudes.

Relationship between Radius and Volume

For a sphere, the volume is determined by the formula V = (4/3)?r³, indicating that the volume scales with the cube of the radius. This cubic relationship is critical because even minor changes in the radius can lead to significant changes in volume. This concept is essential in understanding the physical implications of size alterations in spherical bodies, such as planets.

Relationship between Radius and Circumference

The circumference of a circle, given by the formula C = 2?r, is directly proportional to its radius. This relationship is key when analyzing how variations in the radius lead to changes in the circumference. Understanding this proportionality is fundamental in geometry and astrophysics, as it allows one to calculate the effect of a small change in radius on the overall size of a circular or spherical object.

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