Final answer:
To find Jupiter's sidereal period given its synodic period of 1.092 years, we use the relationship between the synodic and sidereal periods. After calculations, the sidereal period of Jupiter is found to be approximately 11.87 years.
Step-by-step explanation:
To determine Jupiter's sidereal period, we need to use its synodic period and the orbital period of the Earth around the Sun. The synodic period is the time it takes for a planet to return to the same position relative to the Earth and Sun. Because Jupiter and Earth are both orbiting the Sun, we can calculate the sidereal period using the following relation:
1 / Psyn = 1 / Pearth - 1 / Pjup
Here, Psyn is the synodic period of Jupiter (1.092 years), Pearth is Earth's orbital period (1 year), and Pjup is Jupiter's sidereal period, which we are trying to find.
Solving for Pjup:
1 / Pjup = 1 / 1 year - 1 / 1.092 years
1 / Pjup = (1.092 - 1) / (1.092)
1 / Pjup = 0.092 / 1.092
Pjup = 1.092 / 0.092
Pjup ≈ 11.87 years
Therefore, Jupiter's sidereal period is approximately 11.87 years.