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CSET Science (118, 119) Practice Tests & Test Prep by Exam Edge - Free Test


Our free CSET Science (118, 119) Practice Test was created by experienced educators who designed them to align with the official California Teacher Certification content guidelines. They were built to accurately mirror the real exam's structure, coverage of topics, difficulty, and types of questions.

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CSET Science - Free Test Sample Questions

If the distance between the Earth and the Sun were half its present value, what would be the number of days in a year?

Correct Answer:
129
to understand how the number of days in a year would change if the distance between the earth and the sun were halved, we can use kepler's third law of planetary motion. this law states that the square of the orbital period (t) of a planet is proportional to the cube of the semi-major axis of its orbit (r), expressed mathematically as \( t^2 \propto r^3 \).

let's denote the current orbital period of the earth as \( t_1 \) (which is approximately 365 days) and the current average distance from the earth to the sun as \( r_1 \). if this distance is halved, the new distance \( r_2 \) will be \( r_1/2 \).

based on kepler's law, we know: \[ \frac{t_1^2}{r_1^3} = \frac{t_2^2}{r_2^3} \] where \( t_2 \) is the new orbital period when the distance is halved. substituting \( r_2 = r_1/2 \) into the equation, we get: \[ \frac{t_1^2}{r_1^3} = \frac{t_2^2}{(r_1/2)^3} \] \[ \frac{t_1^2}{r_1^3} = \frac{t_2^2}{r_1^3/8} \] \[ t_1^2 = \frac{t_2^2}{1/8} \] \[ t_1^2 = 8t_2^2 \] \[ t_2^2 = \frac{t_1^2}{8} \] \[ t_2 = \frac{t_1}{\sqrt{8}} \] \[ t_2 = \frac{t_1}{2\sqrt{2}} \]

since \( \sqrt{2} \approx 1.414 \), we can simplify \( 2\sqrt{2} \) to approximately 2.828. therefore: \[ t_2 \approx \frac{365 \text{ days}}{2.828} \approx 129 \text{ days} \]

this calculation shows that if the distance between the earth and the sun were halved, the orbital period or the length of the year would decrease to approximately 129 days. this significant decrease in the orbital period is due to the much stronger gravitational pull exerted by the sun at the closer distance, causing the earth to travel faster in its orbit.