Which of the following statements or expressions is most nearly associated with Kepler's First Law of Planetary Motion?
A. [tex]P^2=A^3[/tex]
B. Planetary orbits are in the shape of an ellipse.
C. A planet moves fastest when it is farthest from the sun.
D. The distance to a planet is proportional to the time it takes the planet to complete an orbit.
Answer (2)
Kepler's First Law describes the shape of planetary orbits.
It states that planets orbit the Sun in an ellipse, with the Sun at one focus.
Other options relate to different laws or are incorrect.
The correct answer is that planetary orbits are ellipses. Planetary orbits are in the shape of an ellipse.
Explanation
Analyze the options Kepler's First Law of Planetary Motion states that the orbits of planets around the Sun are ellipses, with the Sun at one focus of the ellipse. Let's examine the given options:
P 2 = A 3 : This is Kepler's Third Law, relating the period of an orbit ( P ) to the semi-major axis ( A ) of the ellipse.
Planetary orbits are in the shape of an ellipse: This is Kepler's First Law.
A planet moves fastest when it is farthest from the sun: This statement is incorrect. A planet moves fastest when it is closest to the Sun (perihelion) and slowest when it is farthest from the Sun (aphelion). This is related to Kepler's Second Law (Law of Equal Areas).
The distance to a planet is proportional to the time it takes the planet to complete an orbit: This is not a precise statement of any of Kepler's Laws. Kepler's Third Law provides a more accurate relationship between orbital period and distance.
Identify the correct statement The statement that is most nearly associated with Kepler's First Law of Planetary Motion is:
Planetary orbits are in the shape of an ellipse.
Examples
Kepler's First Law is crucial in space mission planning. For example, when sending a satellite to orbit Earth, engineers must account for the elliptical shape of the orbit to accurately predict the satellite's position and speed at any given time. Understanding that orbits aren't perfect circles helps in designing efficient trajectories and ensuring the satellite's long-term stability in its orbit. This principle also applies to understanding the paths of comets and asteroids in our solar system.
Kepler's First Law states that planetary orbits are in the shape of an ellipse with the Sun at one focus. The correct choice related to this law is option B. Other options relate to Kepler's Second and Third Laws or are incorrect interpretations.
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