Thank you for visiting The orbit of Eris has a maximum distance of 97 7 AU from the sun If the albedo is 0 8 what is the average. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
The average temperature of Eris when it's farthest from the Sun can be calculated using Stephan's law and the inverse square law. Considering the high albedo and distance of Eris from the Sun, the temperature is found to be approximately 28.2 Kelvin.
Explanation:
The average temperature of Eris when it's farthest from the sun can be calculated using Stephan's law, disregarding any internal heat the planet might have. Stephan's law states that the power radiated per unit area of a black body is proportional to the fourth power of its temperature. Let's perform the calculations step-by-step:
- First, we find the equivalent temperature of the planet if it was at 1 AU (average distance from Earth to the Sun) from the Sun. This can be calculated using the formula: T = (S * (1 - A) / (4 * σ))^0.25, where S is the solar constant (average insolation), A is the albedo of the planet, and σ is the Stefan-Boltzmann constant. We get T1 = (1361 W/m² * (1 - 0.8) / (4 * 5.67x10â»â¸ W/m² Kâ´))^0.25 ≈ 279.3 K.
- Then, we correct this temperature for the actual distance of Eris from the Sun, by scaling it down using the inverse square law, as the intensity of the Sun's radiation decreases with the square of the distance from it. We get T2 = T1 / sq_root(97.7) ≈ 28.2 K. So, the average temperature of Eris when it's farthest from the Sun would be around 28.2 Kelvin.
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