How critical is the Earth-Sun distance in maintaining our average temperatures on Earth?
The distance between Earth and Sun is probably the least critical with respect to the average temperatures on Earth. The distance between Earth and Sun is about 92 million miles and the change in distance due to the eccentric orbit of Earth around the Sun is around 3 million miles. This is a small percent of the actual distance between the Earth and the Sun, and will hence not cause an appreciable change in the average temperature (especially when considering the actual change in temperature on account of seasons).
Further, the temperature on Earth is also dependent on other factors. If one calculates the equilibrium temperature on Earth based on energy balance, then one will find that it comes to around 0 F, which is quite cold. The reason why the Earth is warm at about 70 F is because of other factors like greenhouse effect. There is a common misconception that the greenhouse effect is something really bad. The truth is that it is because of a mild greenhouse effect that Earth is as warm as it is. It is when the greenhouse effect starts becoming a runaway process that it becomes a cause for concern, but we are moving in that direction with the burning of fossil fuels.
In addition, Earth's geological activity also affects the average temperatures. As a simple example, if there is a massive volcanic eruption that sends large amounts of dust into the atmosphere, then the dust could block sunlight thereby cooling the Earth. Another factor that affects climate and temperatures on Earth is variations in the solar luminosity.
So, while large changes in the distance between Earth and Sun would of course affect the average temperature on Earth, variations that are a small percentage of the actual distance will not have any appreciable effect.
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