We observe that oppositions of Saturn repeat every 378 days. Use this information to find the sidereal period of Saturn. Express your answer in years and round to two significant digits.
To find the sidereal period of Saturn, we need to determine the time it takes for Saturn to complete one full orbit around the Sun.
We know that oppositions of Saturn repeat every 378 days. An opposition occurs when Earth, Saturn, and the Sun are in a straight line, with Earth being in the middle. During an opposition, Saturn is visible throughout the night and rises opposite to the Sun.
Since an opposition happens when Earth and Saturn are in a straight line with the Sun, it means that Earth and Saturn are at their closest point. In other words, at opposition, Saturn is at opposition to the Sun.
Now, let's consider this scenario: Earth, Saturn, and the Sun are in a straight line, and Saturn is at opposition to the Sun. If we advance one full orbit around the Sun, Earth will again be in the same position relative to the Sun, and Saturn will also return to opposition.
Therefore, the time it takes for Saturn to complete one full orbit around the Sun is equal to the time between two oppositions, which is 378 days.
To convert this time to years, we divide 378 days by the number of days in a year. Considering that a year consists of approximately 365.24 days, we can calculate the sidereal period of Saturn as follows:
Sidereal Period = 378 days / 365.24 days/year
Sidereal Period ≈ 1.035 years
Rounding to two significant digits, the sidereal period of Saturn is approximately 1.04 years.