Answer :
To determine which planet revolves at a higher speed around the sun, we need to consider the gravitational force acting on each planet. The force of gravity is given by the equation \( F = \frac{G \cdot m_1 \cdot m_2}{r^2} \), where \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two objects, and \( r \) is the distance between them. Because gravitational force is inversely proportional to the square of the distance \( r \), the closer a planet is to the Sun, the stronger the gravitational pull it experiences.
For Planet Y, which is at a distance of 1 AU from the Sun:
[tex]\[ F_Y = \frac{1}{(1)^2} = 1.0 \text{ (arbitrary units)} \][/tex]
For Planet Z, which is at a distance of 0.39 AU from the Sun:
[tex]\[ F_Z = \frac{1}{(0.39)^2} \approx 6.575 \text{ (arbitrary units)} \][/tex]
From these calculations:
1. The gravitational force experienced by Planet Y is \( 1.0 \) arbitrary units.
2. The gravitational force experienced by Planet Z is approximately \( 6.575 \) arbitrary units.
Since Planet Z is closer to the Sun, it experiences a stronger gravitational force compared to Planet Y. The stronger gravitational force on Planet Z means it must travel at a higher speed to maintain its orbit. Thus, Planet Z revolves at a higher speed around the Sun.
Therefore, the statement that best explains which planet revolves at a higher speed is:
Planet Z, because the gravitational force is strengthened by distance.
For Planet Y, which is at a distance of 1 AU from the Sun:
[tex]\[ F_Y = \frac{1}{(1)^2} = 1.0 \text{ (arbitrary units)} \][/tex]
For Planet Z, which is at a distance of 0.39 AU from the Sun:
[tex]\[ F_Z = \frac{1}{(0.39)^2} \approx 6.575 \text{ (arbitrary units)} \][/tex]
From these calculations:
1. The gravitational force experienced by Planet Y is \( 1.0 \) arbitrary units.
2. The gravitational force experienced by Planet Z is approximately \( 6.575 \) arbitrary units.
Since Planet Z is closer to the Sun, it experiences a stronger gravitational force compared to Planet Y. The stronger gravitational force on Planet Z means it must travel at a higher speed to maintain its orbit. Thus, Planet Z revolves at a higher speed around the Sun.
Therefore, the statement that best explains which planet revolves at a higher speed is:
Planet Z, because the gravitational force is strengthened by distance.
