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## Homework Statement

If we were to put a spacecraft into orbit around the Sun at a distance of 0.900 au and then gradually increase the orbital distance closer and closer to 1 au, what would happen to the synodic period of the spacecraft? Why does this happen?

## Homework Equations

1/S = 1/P - 1/E & P2 = a3

## The Attempt at a Solution

I get the correct answer when i calculate the known planets, mercury, venus, mars... but my hypothetical planets (orbiting the Sun) are just shy of 1au and just beyond 1au. example planet D (a=0.999) with this formula i get 665.833...(calculating in years) using this 1/s = 1/.9985-1/1. .9985 is what i got with P2 = a3. However when i replace 1/e (earth) with 365.26 and convert that to years it seems reasonable, being 1.001. One explanation has this statement "taking the limit of S as P approaches 1 AU", i just cant seem to find an explanation anywhere on the web. Does this formula break down closer to 1 because we use the earth as a reference, or am i just using it incorrectly. Please tell me if this is confusing and i will try to explain it better. Thank you!!