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Chapter 4: Problem 17

A line joining the Sun and an asteroid is found to sweep out an area of \(6.3 \mathrm{AU}^{2}\) during 2010 . How much area is swept out during 2011? Over a period of five years?

Short Answer

Expert verified
The area swept out during 2011 is \(6.3 \, \mathrm{AU}^{2}\). The area swept out in a period of 5 years is \(31.5 \, \mathrm{AU}^{2}\).

Step by step solution

01

Understanding Kepler's Second Law of equal areas

Firstly we need to understand that according to Kepler's Second Law, the line joining the Sun and a celestial body such as a planet or an asteroid would cover equal areas over equal intervals of time. So, if a certain area is swept in a year then, this will be the same for the next year (assuming there's no any other outer influence), as the time interval is equal.
02

Calculate the area swept out during 2011

Since the time interval is the same, we know that the area swept out during 2011 will be the same as the area swept out during 2010. Therefore, the area swept out during 2011 will also be \(6.3 \, \mathrm{AU}^{2}\).
03

Calculate the area swept out over a period of five years

For a period of five years, we simply multiply the area swept out in one year by 5. Therefore, the area swept out over a period of 5 years = \( 6.3 \, \mathrm{AU}^{2} \times 5 = 31.5 \, \mathrm{AU}^{2}\).

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