The image and document you've shared are from an activity related to scaling distances in the universe. The task shown in the image asks two questions:

1. What is the radius of your home planet?
2. How many seconds would it take light to travel this distance?

How to solve:

1. Radius of the Home Planet:

• The "view of the sky" is given as 20,000 km across, which represents the diameter of the planet.
• To find the radius (which is half the diameter), we can use the formula: $\text{Radius} = \frac{\text{Diameter}}{2} = \frac{20,000 \text{ km}}{2} = 10,000 \text{ km}.$

2. Time for Light to Travel the Radius:

• The speed of light is approximately $3.00 \times 10^5$ km/s.
• To find how long it would take for light to travel the planet's radius (10,000 km), use the formula for time: $t = \frac{d}{v},$ where $d$ is the distance (10,000 km), and $v$ is the speed of light (300,000 km/s). So: $t = \frac{10,000 \text{ km}}{300,000 \text{ km/s}} = \frac{1}{30} \text{ s} \approx 0.033 \text{ s}.$

Therefore:

• The radius of your home planet is 10,000 km.
• It would take light approximately 0.033 seconds to travel that distance.

Let me know if you'd like more details or have any questions!

Here are five related questions you can explore next:

1. How does the speed of light affect time calculations for larger astronomical distances?
2. What is the average radius of other planets in the solar system compared to Earth?
3. How would the time for light to travel change if the distance was doubled?
4. How does the concept of light-years help in measuring vast distances in the universe?
5. What are the consequences of the finite speed of light in observing distant astronomical objects?

Tip: For longer astronomical distances, using light-years instead of kilometers simplifies the scale. One light-year is the distance light travels in one year, approximately 9.46 trillion kilometers.