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Semi-major axis, sidereal period and synodic period of a hypothetical planet

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A hypothetical planet travels in an elliptical orbit around the Sun. The perihelion distance is 2.65 AU and the aphelion distance is 2.85 AU. For this hypothetical planet determine:

a) the semi-major axis of its orbit.
b) the sidereal period.
c) the synodic period as seen from the Earth.

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The expert examines sidereal periods and synodic period of a hypothetical planet.

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Please see the attached. I have used 2 methods to produce the sidereal period in SI units using Newtonian mechanics and an equivalent sidereal period for the planets using Kepler's 3rd Law. You will see references as well as further resources.

(a) Semi Major Axis which we denote as for the elliptical orbit is iust the avarge of the sum of the perihelion distance and the aphelion distance . This can be seen from the geometry so we can write

Putting in values where and we get

We need to convert this to SI units so to ...

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