Why could earth not support life if it was a smaller planet?

Answer:

Smaller planets would dissipate heat more rapidly and this criteria doesn't satisfy the conditions of existence of life.

Explanation:

The existence of life on Earth was possible because it fulfilled the criteria needed for the conditions of generating life in a planet. Its distance from sun is appropriate, it is made up of rock, it is big enough to have a core which is molten and it has a magnetic field. If it was a smaller planet, then it would have a liquid hot core that dissipate heat at a rapid rate. This condition doesn't support the criteria of life's existence.

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b - the respond is innate and varies over time.

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