Based on Kepler's observations about planetary motion, what is the relationship between a planet's orbital velocity and its distance from the sun? *
1 point
a. The greater the distance, the slower the orbital velocity.
b. Distance has no effect on orbital velocity.
c. The greater the distance, the greater the orbital velocity.
d. As distance is cut in half, orbital velocity decreases.
a. The greater the distance, the slower the orbital velocity.
To determine the relationship between a planet's orbital velocity and its distance from the sun based on Kepler's observations, we need to refer to Kepler's laws of planetary motion. Let's break down the options:
a. The greater the distance, the slower the orbital velocity.
- This option aligns with Kepler's observations which indicate that planets have slower orbital velocities as their distances from the sun increase. Planets farther from the sun experience weaker gravitational forces, resulting in slower orbital velocities.
b. Distance has no effect on orbital velocity.
- This option contradicts Kepler's observations. According to Kepler's laws, a planet's distance from the sun indeed affects its orbital velocity.
c. The greater the distance, the greater the orbital velocity.
- This option is incorrect. Kepler's observations show that the opposite is true: the greater the distance, the slower the orbital velocity.
d. As distance is cut in half, orbital velocity decreases.
- This option is the most accurate. According to Kepler's third law, the square of a planet's orbital period is directly proportional to the cube of its semi-major axis (which represents the distance between the planet and the sun). If the distance (semi-major axis) is halved, the orbital period will be reduced to one-eighth, and consequently, the orbital velocity will decrease.
Therefore, option d is the correct answer: As distance is cut in half, orbital velocity decreases.