Explain how we know that the Sun's energy is not supplied either by chemical burning, as in fires here on Earth, or by gravitational contraction (shrinking).

The vast amount of energy produced by the Sun over the past 4.5 billion years exceeds the amount that could be supplied by burning or shrinking of the Sun by a significant factor. Chemical burning would only last a few thousand years, whereas gravitational contraction would provide energy for only about a hundred million years. but we can confidently say the sun gets its energy from matter that is converted into energy through the fusion of hydrogen into helium.