The relation for calculating the synodic period of two bodies is rather simple

If the orbital periods of the two bodies around the third are called $T_1$ and $T_2$, so that $T_1 < T_2$, their synodic period is given by: $1 \over T_{syn}$$=$$1 \over T_1$$-$$1 \over T_2$

The relationship between orbital radius and orbital period is given by $T= 2\pi\sqrt{a^3/GM}$

Wolphram Alpha helps calculating that:

• 10 million miles are 0.1 au
• the orbital period at 1.1 au would be 421.4 days
• the orbital period at 0.734 au would be 229.7 days

therefore the synodic period, based on the formula above, would be 504.9 days

The relation for calculating the synodic period of two bodies is rather simple

If the orbital periods of the two bodies around the third are called $T_1$ and $T_2$, so that $T_1 < T_2$, their synodic period is given by: $1 \over T_{syn}$$=$$1 \over T_1$$-$$1 \over T_2$

The relationship between orbital radius and orbital period is given by $T= 2\pi\sqrt{a^3/GM}$

Wolphram Alpha helps calculating that:

• 10 million miles are 0.1 au
• the orbital period at 1.1 au would be 421.4 days
• the orbital period at 0.824 au would be 273.2 days

therefore the synodic period, based on the formula above, would be 776.8 days

The relation for calculating the synodic period of two bodies is rather simple

If the orbital periods of the two bodies around the third are called $T_1$ and $T_2$, so that $T_1 < T_2$, their synodic period is given by: $1 \over T_syn$$=$$1 \over T_1$$-$$1 \over T_2$

The relationship between orbital radius and orbital period is given by $T= 2\pi\sqrt{a^3/GM}$

Wolphram Alpha helps calculating that:

• 10 million miles are 0.1 au
• the orbital period at 1.1 au would be 421.4 days
• the orbital period at 0.734 au would be 229.7 days

therefore the synodic period, based on the formula above, would be 504.9 days

The relation for calculating the synodic period of two bodies is rather simple

If the orbital periods of the two bodies around the third are called $T_1$ and $T_2$, so that $T_1 < T_2$, their synodic period is given by: $1 \over T_{syn}$$=$$1 \over T_1$$-$$1 \over T_2$

The relationship between orbital radius and orbital period is given by $T= 2\pi\sqrt{a^3/GM}$

Wolphram Alpha helps calculating that:

• 10 million miles are 0.1 au
• the orbital period at 1.1 au would be 421.4 days
• the orbital period at 0.734 au would be 229.7 days

therefore the synodic period, based on the formula above, would be 504.9 days