Which quantities decrease as the distance between a planet and the Sun increases?

A. tangential speed
B. mass
C. gravitational force
D. area swept out in a day
E. distance traveled in a day

Tangential speed decreases as the distance from the Sun increases due to Kepler's Second Law.
Mass remains constant regardless of the distance from the Sun.
Gravitational force decreases as the distance increases, according to Newton's Law of Universal Gravitation: F = G \tims r 2 m 1 ​ \tims m 2 ​ ​ .
Distance traveled in a day decreases as the tangential speed decreases.
The quantities that decrease are tangential speed, gravitational force, and distance traveled in a day.

Explanation

Problem Analysis We need to determine which of the given quantities decrease as the distance between a planet and the Sun increases. Let's analyze each quantity:

Tangential Speed

Tangential speed: According to Kepler's Second Law, planets move faster when they are closer to the Sun and slower when they are farther away. Therefore, tangential speed decreases as the distance increases.

Mass

Mass: The mass of a planet is an intrinsic property and does not depend on its distance from the Sun. The mass remains constant.

Gravitational Force

Gravitational force: According to Newton's Law of Universal Gravitation, the gravitational force ( F ) between two objects is inversely proportional to the square of the distance ( r ) between them: F = G \tims r 2 m 1 ​ \tims m 2 ​ ​ where G is the gravitational constant, m 1 ​ and m 2 ​ are the masses of the two objects. Therefore, as the distance r increases, the gravitational force F decreases.

Area Swept Out

Area swept out in a day: Kepler's Second Law states that a planet sweeps out equal areas in equal times. Therefore, the area swept out in a day is constant and does not depend on the distance.

Distance Traveled

Distance traveled in a day: Since the tangential speed decreases as the distance increases, the distance traveled in a day also decreases.

Conclusion Therefore, the quantities that decrease as the distance between a planet and the Sun increases are tangential speed, gravitational force, and distance traveled in a day.


Examples
Understanding how quantities change with distance from the Sun is crucial in space mission planning. For example, when sending a probe to a distant planet, engineers must account for the decreasing gravitational force to calculate the probe's trajectory and speed accurately. Similarly, the changing tangential speed affects the time it takes for the probe to reach its destination. Kepler's laws and Newton's law of gravitation are fundamental in these calculations, ensuring successful mission outcomes.

Answered by GinnyAnswer | 2025-07-03

As the distance between a planet and the Sun increases, the tangential speed, gravitational force, and distance traveled in a day decrease. Mass remains constant, and the area swept out in a day does not change. The correct options are A, C, and E.
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Answered by Anonymous | 2025-07-04