A spacecraft starts on Earth is moving to Mars. Which of the following is correct about the gravitational force on the spacecraft due to Earth’s attraction?

Question

BlackTom AI · Accepted Answer

Newton’s law of universal gravitation: F = G M_e m / r^2, so the Earth’s pull on the spacecraft falls off with the square of the distance r from Earth’s center but does not become exactly zero at any finite r.

1) Relevant concepts
- Gravitational force magnitude: F = G M_e m / r^2 (G = 6.674×10^-11 N·m^2/kg^2, M_e ≈ 5.97×10^24 kg).
- The force decreases continuously as distance increases and approaches zero only in the limit r → ∞.
- “Net” force can be zero where multiple bodies’ pulls cancel, but the Earth’s individual contribution at that point is still nonzero.

2) Step-by-step reasoning
- At Earth’s surface, r = R_e ≈ 6.37×10^6 m: acceleration a = GM_e / R_e^2 ≈ 9.81 m/s^2.
- Move the spacecraft outward: r increases, so F decreases as 1/r^2, but remains positive for any finite r.
- Even at Mars distances the Earth’s pull is tiny but nonzero.

3) Numerical example (intermediate steps)
- GM_e ≈ 3.986×10^14 m^3/s^2.
- If Earth–Mars separation ~0.5 AU ≈ 7.5×10^10 m, then a = GM_e / r^2 = 3.986×10^14 / (7.5×10^10)^2.
- Denominator = (7.5×10^10)^2 = 5.625×10^21, so a ≈ 3.986×10^14 / 5.625×10^21 ≈ 7.1×10^-8 m/s^2 — very small but not zero.

4) Why the correct answer is correct
- Because gravity from a mass falls off with distance but does not abruptly stop at some boundary (atmosphere, halfway point, planet surface). Only at infinite separation would Earth’s gravitational force strictly be zero.

5) Why other options are incorrect
- a and c: landing on Mars or being closer to Mars does not make Earth’s gravitational force zero; Mars’ gravity adds but does not nullify Earth’s contribution.
- d: “halfway” has no physical basis; cancellation points depend on masses and distances, not midpoint.
- e: leaving the atmosphere does not remove Earth’s gravity — gravity acts well beyond the atmosphere.

6) Conclusion
The spacecraft is never beyond the Earth’s gravitational attraction (option b). This matches the provided correct answer.

A spacecraft starts on Earth is moving to Mars. Which of the following is correct about the gravitational force on the spacecraft due to Earth’s attraction?单项选择题

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