(Lesson 7.02)
A planet with a warm temperature would have a (blank) .

Question

(Lesson 7.02)
A planet with a warm temperature would have a   (blank)  .

BlackTom AI · Accepted Answer

Planetary equilibrium temperature is set by the balance between incoming stellar radiation and outgoing thermal radiation. The stellar flux at the planet is F = L / (4πd^2), where L is the star’s luminosity and d is the star–planet distance. The planet’s equilibrium temperature Teq (ignoring greenhouse effects) follows from Stefan–Boltzmann balance:
Teq = [L (1 − A) / (16 π σ d^2)]^(1/4),
where A is albedo and σ is the Stefan–Boltzmann constant.

Step-by-step reasoning:
1. Start with the flux: incoming power per unit area ∝ L / d^2. Doubling L doubles the incoming flux; moving twice as far reduces flux by 4.
2. The planet absorbs a fraction (1 − A) of that flux (A = albedo), so absorbed power ∝ L(1 − A)/d^2.
3. The planet radiates as a blackbody: outgoing power ∝ σTeq^4. Setting absorbed = emitted gives the equilibrium formula above.
4. Solve for Teq dependence on L: Teq ∝ L^(1/4) (holding d and A constant). Thus a higher stellar luminosity increases Teq; for example, if L increases by a factor of 16, Teq increases by 16^(1/4) = 2 (twice as hot in Kelvin scale factor for equilibrium temperature).

Why the correct answer is “high star luminosity”:
- Because Teq scales with L^(1/4), a more luminous star delivers more energy and raises the planet’s equilibrium temperature, making it warmer under the same distance and albedo conditions.

Why other plausible factors are not the best choice:
- Greater orbital distance lowers flux (Teq ∝ 1/d^(1/2)), so it makes planets colder, not warmer.
- Planetary size (radius or mass) does not directly set equilibrium temperature; it affects gravity/atmosphere retention but not the basic radiative balance.
- Albedo and greenhouse effects do affect temperature (low albedo or strong greenhouse warming can warm a planet), but the primary direct determinant in this context is stellar luminosity.

Conclusion: A planet with a warm temperature would have a high star luminosity, which matches the provided correct answer.

(Lesson 7.02) A planet with a warm temperature would have a (blank) .单项选择题

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