Let us say that Earth and Venus are both moved 10 million additional miles from the sun. How would the synodic period of Venus appear to change for an observer on Earth? If 584 days is Venus' current synodic period, how many days would elapse if the planets were adjusted as mentioned?
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1$\begingroup$ This is a question for Astronomy.SE. I am confident they can help you. $\endgroup$– TomCommented Aug 18, 2022 at 16:59
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$\begingroup$ In all SE network it helps if you show what have you searched on your own. Being just a couple of formulas that you need, you might find the answer on your own. $\endgroup$– L.Dutch ♦Commented Aug 18, 2022 at 17:10
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$\begingroup$ Thank you for these helpful comments! $\endgroup$– JM YadenCommented Aug 18, 2022 at 17:14
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1 Answer
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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
answered Aug 18, 2022 at 17:24
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$\begingroup$ This is marvelous, thank you so much for showing the math here and solving. I will do the calculations myself using these formulas and make sure I can do it. Much appreciated, L.Dutch! <3 $\endgroup$– JM YadenCommented Aug 18, 2022 at 17:29