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The problem involves calculating the orbital speed of a satellite in both **km/h** and **m/s**, given that:

- The satellite's orbit radius is 8000 km.
- The time period for one complete orbit is 120 minutes.

### Steps to Solve:

#### 1. **Convert the radius to meters:**
The radius of the orbit \( r = 8000 \, \text{km} \).
\[
r = 8000 \times 1000 = 8,000,000 \, \text{m}
\]

#### 2. **Convert the time period to seconds:**
The time period \( T = 120 \, \text{minutes} \).
\[
T = 120 \times 60 = 7200 \, \text{seconds}
\]

#### 3. **Calculate the circumference of the orbit:**
The satellite travels in a circular orbit, so the distance it covers in one orbit is the circumference of the circle:
\[
C = 2 \pi r = 2 \pi \times 8,000,000 \, \text{m} \approx 50,265,482 \, \text{m}
\]

#### 4. **Calculate the orbital speed:**

- **In meters per second (m/s):**
The speed \( v \) is the distance covered per unit of time:
\[
v = \frac{C}{T} = \frac{50,265,482 \, \text{m}}{7200 \, \text{s}} \approx 6981.31 \, \text{m/s}
\]

- **In kilometers per hour (km/h):**
First, convert the speed from m/s to km/h:
\[
v_{\text{km/h}} = v_{\text{m/s}} \times 3.6 = 6981.31 \times 3.6 \approx 25,332.71 \, \text{km/h}
\]

### Final Answer:
- **a. Orbital speed in km/h:** \( 25,332.71 \, \text{km/h} \)
- **b. Orbital speed in m/s:** \( 6981.31 \, \text{m/s} \)

Would you like further details or have any questions?

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Here are 5 related questions:
1. How does the altitude of a satellite affect its orbital speed?
2. How would the time period change if the radius of the orbit were doubled?
3. What is the relationship between orbital radius and velocity in circular orbits?
4. How can you derive the speed of a satellite using gravitational forces?
5. What is the significance of the geostationary orbit for satellites?

**Tip:** When working with orbital problems, always ensure that units are consistent (e.g., seconds for time, meters for distance) to avoid calculation errors.

A satellite moves around the Earth at constant speed on a circular orbit of radius 8000 km with a time period of 120 min. Calculate its orbital speed in a. km h^−1 b. m s^−1

Learn how to calculate the orbital speed of a satellite moving in a circular orbit with a radius of 8000 km and a time period of 120 minutes. This solution explains the key steps including converting units and applying formulas for orbital mechanics.

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