Question

How does the mass of and distance between the Sun and the Earth impact the number of days in a year?

Answer 1

Force of sun on earth can be written:

F = G M m / R^2

Centripetal force on earth can be written:

F= m w^2 R

Equating these:

G M / R^2 = w^2 R

Or w^2 = G (M / R^3)

Since no/ days per year is proportional to w (time for 1 revolution)

Increasing M (mass of sun) would increase w or decrease length of year

Increasing the mean radius R would decrease w or increase length of year