An artificial satellite is moving in a circular orbit of radius `42250 km`. Calculate its speed if it takes `24 hours` to revolve around the Earth.

Explanation

To solve the problem of calculating the speed of an artificial satellite moving in a circular orbit, we can follow these steps:

### Step 1: Understand the Given Information
- Radius of the circular orbit (r) = 42250 km
- Time taken for one complete revolution (T) = 24 hours

### Step 2: Convert Time to Seconds
Since speed is usually calculated in meters per second (m/s), we should convert the time from hours to seconds.
\[ T = 24 \text{ hours} = 24 \times 60 \times 60 \text{ seconds} = 86400 \text{ seconds} \]

### Step 3: Calculate the Angular Velocity (ω)
The angular velocity (ω) can be calculated using the formula:
\[ \omega = \frac{2\pi}{T} \]
Substituting the value of T:
\[ \omega = \frac{2\pi}{86400} \text{ radians per second} \]

### Step 4: Calculate the Linear Speed (v)
The linear speed (v) of the satellite can be calculated using the formula:
\[ v = \omega \times r \]
Substituting the values of ω and r:
\[ v = \left(\frac{2\pi}{86400}\right) \times 42250 \text{ km} \]

### Step 5: Simplify the Expression
Calculating the above expression:
\[ v = \frac{2 \times 3.14 \times 42250}{86400} \text{ km/s} \]
\[ v = \frac{265,000}{86400} \text{ km/s} \]
\[ v \approx 3.07 \text{ km/s} \]

### Step 6: Convert Speed to km/h
To convert the speed from km/s to km/h, multiply by 3600 (since 1 hour = 3600 seconds):
\[ v \approx 3.07 \times 3600 \text{ km/h} \approx 11000 \text{ km/h} \]

### Final Answer
The speed of the artificial satellite is approximately **11000 km/h**.

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