Answer:
A. True
Explanation:
To determine whether the acceleration of a planet is at its maximum when it is closest to the sun, we need to consider the principles of orbital mechanics and Kepler's laws of planetary motion.
According to Kepler's second law, a planet moves faster in its orbit when it is closer to the sun (at perihelion) and slower when it is farther from the sun (at aphelion). The gravitational force exerted by the sun on the planet is stronger when the planet is closer to the sun due to the inverse-square law of gravitation:
[tex]\boxed{ \begin{array}{ccc}\text{\underline{Newton's Law of Universal Gravitation:}} \\\\ F = G \dfrac{m_1 m_2}{r^2} \\\\\text{Where:} \\\bullet \ F \ \text{is the gravitational force between two masses} \\\bullet \ G \ \text{is the gravitational constant} \ (6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2) \\\bullet \ m_1 \ \text{and} \ m_2 \ \text{are the masses of the objects} \\\bullet \ r \ \text{is the distance between the centers of the two masses}\end{array} }[/tex]
The acceleration 'a' of the planet is given by Newton's second law:
[tex]a=\dfrac{F}{m} = G \dfrac{m_1 m_2}{r^2}[/tex]
As 'r' decreases, the value of 'a' increases. Hence, the planet's acceleration is indeed at its maximum when it is closest to the sun.
Thus, the answer is:
A. True