1. Earth's acceleration during eclipses.
What is the percentage change in the acceleration of Earth toward the Sun when the alignment of Earth, Sun, and Moon changes from an eclipse of the Sun (with the moon between Earth and Sun) to an eclipse of the Moon (Earth between Moon and Sun)?
Assume that Earth's orbital path around the Sun is a perfect circle and that the Moon's orbital path around Earth is also a perfect circle, in the same plane. Also assume that the Moon orbits around Earth's center of mass and Earth orbits around the Sun's center of mass. (Although none of these assumptions are actually true, they are not far off.)
2. Twin Sun system.
In a hypothetical binary star system, each star has the same mass as our Sun, and they revolve about their center of mass. Their orbit is perfectly circular, so that the distance between them is always exactly twice the distance between Earth and our Sun. What is the period of the stars' rotation?