Question

the image shows how earth orbits the sun. points w and x are the same distance from the sun. which conclusion is best supported by the image? earth is speeding up at w and slowing down at x because the force on earth is greater at w than at x. earth is slowing down at w and speeding up at x because the force on earth is greater at w than at x. the speed of earth is the same at w as at x because the force on earth is the same at w as at x. the speed of earth is greater at w than at x because the force on earth is greater at w than at x.

Explanation:

1. Gravitational Force and Distance: The Sun exerts a gravitational force on Earth. According to the inverse - square law of gravitation ($F = G\frac{Mm}{r^{2}}$), where $F$ is the gravitational force, $G$ is the gravitational constant, $M$ is the mass of the Sun, $m$ is the mass of the Earth, and $r$ is the distance between the Sun and the Earth. When the Earth is closer to the Sun (at a point like W, assuming the left - most point is the perihelion), the distance $r$ is smaller, so the gravitational force $F$ is larger.
2. Effect of Force on Orbital Speed: According to Kepler's second law (the law of equal areas), a planet moves faster when it is closer to the Sun (where the gravitational force is stronger) and slower when it is farther from the Sun (where the gravitational force is weaker). Since W is closer to the Sun (implied by the diagram's structure, as the lines from the Sun to W are shorter in terms of the angular - related distance for equal - area sweep, or from the inverse - square law reasoning about force and distance) than X (or at least the force at W is greater as W is closer), the Earth's speed at W is greater than at X.

• For the first option: The force is greater at W (closer), so Earth should be speeding up when closer? No, actually, when moving from a farther point to a closer point (towards perihelion), Earth speeds up. But the first option says "speeding up at W and slowing down at X" which is incorrect.
• For the second option: The force is greater at W, so Earth should be moving faster at W (speeding up as it approaches perihelion or moving fast at perihelion - like point W), not slowing down at W. So this is incorrect.
• For the third option: The force is not the same at W and X because their distances from the Sun are the same? Wait, no, the diagram shows that the lines from the Sun to W and X are part of the elliptical orbit. Wait, actually, in an elliptical orbit, the distance from the Sun varies. But the key is that the gravitational force depends on distance. If W is closer, force at W is greater. And the speed is not the same. So this option is incorrect.

Answer:

The fourth option: The speed of Earth is greater at W than at X because the force on Earth is greater at W than at X.