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Which of the following must be true based on gravitational field information?

A) Planet X is larger than Planet Y.
B) Planet Y is more massive than Planet X.
C) Planet X has a higher gravitational potential energy.
D) Planet Y has a lower gravitational potential energy.

1 Answer

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Final answer:

None of the given options A, B, C, or D can be confirmed as true based on the provided gravitational field information without additional context such as the relative positions or masses of Planet X and Planet Y.

Step-by-step explanation:

The response to the question of which statement must be true based on gravitational field information is dependent on the law of universal gravitation, which states that every mass exerts an attractive force on every other mass. This attraction is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

For the given options, none of the statements A, B, D can be determined as true solely based on the information about the gravitational fields. However, statement C implies a relationship between gravitational potential energy, mass, and distance from the gravitational source; without additional context such as relative positions or detailed measurements, this cannot be confirmed as true either.

From the background provided, we know that for two bodies attracting each other gravitationally:

  • The force exerted by each on the other is equal in magnitude and opposite in direction, as per Newton's third law of motion (Option B).
  • If one asteroid has twice the mass of the other, both asteroids experience the same magnitude of gravitational force but the lighter one experiences greater acceleration due to having less mass (Option 25).

When comparing gravitational potential energy, the more massive an object, and the further away it is from another object, the higher the gravitational potential energy. Since Planet X and Planet Y are not described in terms of relative distances or specific masses, no definitive conclusion can be drawn about their gravitational potential energy.

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