Certainly! Let's dive into the problem step-by-step:
### Step 1: Identifying the relevant calendar cycles
- A lunar month is approximately 29.53 days long.
- A solar (or Gregorian) month is approximately 30 days long.
- Therefore, each lunar month is shorter than a solar month, resulting in a difference.
### Step 2: Calculating the difference per month
- We need to find out how much difference there is between one lunar month and one solar month.
[tex]\[
\text{Difference per month} = 30 \text{ days (solar month)} - 29.53 \text{ days (lunar month)} = 0.47 \text{ days}
\][/tex]
### Step 3: Determining the total difference to reach our goal
- We are tasked with determining when the lunar calendar is 30 days behind the solar calendar.
- Our goal difference is 30 days.
### Step 4: Calculating the number of lunar months required to reach this difference
- We can divide the total difference (30 days) by the difference per lunar month to find how many lunar months would pass before accumulating a 30-day lag.
[tex]\[
\text{Number of lunar months} = \frac{30 \text{ days}}{0.47 \text{ days/month}} \approx 63.83 \text{ lunar months}
\][/tex]
### Step 5: Conclusion
Based on the calculations:
- Approximately 63.83 lunar months would pass before the lunar calendar is 30 days behind the solar calendar.
- After every 63.83 lunar months, a leap month should be added to the lunar calendar to keep it in sync with the solar calendar.
In summary, to synchronize the lunar and solar calendars, you should add a leap month approximately every 63.83 lunar months.
