What is the role of conservation of angular momentum?
If the Sun’s rotation slowed down, then the Earth’s rotation would speed up due to conservation of angular momentum. And as the Earth’s rotation speeds up, the Earth’s orbit would gradually spiral away from the Sun. This is what has happened. The period of one solar rotation was about 2 weeks when the Sun was 1 billion years old (Noyes, pg. 26), and now the period of one solar rotation is about 1 month. However, the changes in the increase of Earth’s orbit were, and are, very tiny: In the past, the Earth was orbiting closer to the Sun (centimeters?). Over time, the changes in rotation are less noticeable. During the Sun’s lifetime on the main sequence, the Sun’s rotation has been relatively stable. As time progresses, the rate of transfer of angular momentum becomes less and less, therefore, the Earth “spirals away less and less” due to angular momentum.
