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can you answer these in a step by step procedure please?




Let’s work through the exercise step by step based on the image and lab instructions.

### Part 1: View of Inner Planets

The field of view displayed is currently 200,000,000 km (2 × 10^8 km). Here are the steps to answer the questions:

---

#### **Question 1: What is the radius of your planet's orbit?**

1. **Analyze the grid:**  
   The grid allows you to determine the radius of the planet's orbit. Each square likely represents a specific distance (e.g., 10,000,000 km or 1×10^7 km).

2. **Measure using the grid:**  
   Count the number of squares from the center of the Sun to your planet's position. For example, if the planet is 2 squares away and each square represents 1 × 10^7 km, the radius would be:
   \[
   \text{Radius of orbit} = 2 \times 1 \times 10^7 \, \text{km} = 2 \times 10^7 \, \text{km}
   \]

3. **Determine the radius of your planet's orbit:**  
   Depending on the measurement you get from the grid, this will be the radius in kilometers.

---

#### **Question 2: What is the radius of the orbit of the other planet?**

1. **Identify the other planet:**  
   Locate the second planet’s position on the grid. If it's, say, 4 squares away from the Sun and each square still represents 1 × 10^7 km:

2. **Radius of the other planet’s orbit:**
   \[
   \text{Radius} = 4 \times 1 \times 10^7 \, \text{km} = 4 \times 10^7 \, \text{km}
   \]

---

#### **Question 3: How long would it take light to get to you from the Sun?**

1. **Calculate the distance traveled by light:**  
   Light travels at the speed of 3 × 10^5 km/s. If the radius of your orbit is, say, 2 × 10^7 km (from Question 1), use the formula:
   \[
   t = \frac{d}{v}
   \]
   where:
   - \( d \) is the distance (2 × 10^7 km),
   - \( v \) is the speed of light (3 × 10^5 km/s).

   \[
   t = \frac{2 \times 10^7 \, \text{km}}{3 \times 10^5 \, \text{km/s}} = \frac{2}{3} \times 10^2 \, \text{s} = \frac{200}{3} \, \text{s} \approx 66.67 \, \text{seconds}
   \]

---

These steps will allow you to answer the three questions displayed in the simulation. Would you like to work through more detailed calculations or explanations?

---

### Additional Exercises:

1. What would happen to the radius of orbit measurements if the scale of the grid changes?
2. How does the speed of light influence the time it takes to travel larger distances like to another planet?
3. If the field of view expands further, how would the positions of the planets change visually?
4. What is the relation between the distance to outer planets and their orbital periods?
5. How does the scale of light speed affect our perception of time across astronomical distances?

**Tip:** Always double-check the scale of the grid when making measurements to ensure accuracy in large astronomical units.

can you answer these in a step by step procedure please?

Explore how to calculate the radius of planetary orbits and determine the time it takes light to travel from the Sun using astronomical distances. This guide offers step-by-step solutions with a focus on the Scale of the Universe exercise, perfect for high school students.

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