Let's break down and analyze the images you've provided to extract the relevant data and offer an explanation:

Image 1: Speed of the Car and Celestial Data

1. Speed of the Car:

   • Data provided:
     • Distances and times recorded as the car passes telegraph poles spaced 100 meters apart.
     • Based on the data, the speed of the car is calculated as 40.79 m/s. This value appears in the answer-check form on the right side of the first image.
     • The formula used would be $\text{Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$.

2. Angular Speed of Star:

   • Given: 17.5 degrees per hour.
   • The time-angle relationship for a star is represented by the equation $y = 17.577x + 20.673$ derived from the graph in the second image. Here, the slope of 17.577 matches closely with the angular speed provided (17.5 degrees per hour), confirming the consistency of the calculation.

3. Length of Day:

   • Given: 20.5 hours. This matches the approximate data range in the chart for the star's movement over time.

4. Orbital Period of the Moon:

   • Given: 3.181818 days.
   • From the chart, we observe the equation for the moon's angular movement as $y = 12.075x + 6.9567$, where the slope represents its angular speed. The data also suggest the orbital period is about 3.181818 days, a value corroborated by the calculation.

Image 2: Star and Moon Data

The second image includes graphs representing the angular speed of a star and the moon over time:

1. Star Data:

   • The data on the star shows a nearly linear relationship between time and angle.
   • The equation of the line is $y = 17.577x + 20.673$, where the slope of 17.577 represents the angular speed of the star in degrees per hour, matching the value provided in the first image (17.5 degrees per hour).
   • Based on this, we can confirm the star's angular speed is accurate.

2. Moon Data:

   • The moon's angular data is modeled by the equation $y = 12.075x + 6.9567$, where the slope of 12.075 represents the angular speed of the moon.
   • This data also includes an orbital period of 3.181818 days, matching the provided period in the first image.
   • These values suggest the moon's movement is accurately represented, and the orbital period value is consistent.

Conclusion

The results in both images appear to validate the provided answers:

• The speed of the car (40.79 m/s) seems reasonable given the times and distances.
• The angular speed of the star (17.5 degrees per hour) and its relationship with the time (based on the equation from the graph) align well with the graph's slope.
• The orbital period of the moon (3.181818 days) is consistent across both the numerical and graphical data.

Do you want more details on how to calculate any of these values or need assistance with further calculations?

Additional Questions:

1. How was the speed of the car calculated from the data provided?
2. What is the significance of the angular speed of the star, and how does it relate to the length of the day?
3. How can the equation of the line for the moon's angular speed help calculate the moon's orbital period?
4. Could any errors in data collection impact the calculated values?
5. How would the results change if different assumptions about distances or times were used?

Tip: When graphing data, always ensure to double-check the trend lines and equations to match them with real-world phenomena like angular speed or distance-time relations!