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What is the speed of an artificial satellite moving in a circular orbit of radius 42250 km if it takes 24 hours to revolve around the earth?
- a)2.98 km/s
- b)3.07 km/s
- c)3.02 km/s
- d)3.04 km/s
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
What is the speed of an artificial satellite moving in a circular orbi...
Understanding the Problem
To determine the speed of an artificial satellite in a circular orbit, we will use the formula for orbital speed, which is given by:
\[ v = \frac{2\pi r}{T} \]
where:
- \( v \) = orbital speed
- \( r \) = radius of the orbit
- \( T \) = period of revolution
Given Values
- Radius of the orbit \( r = 42250 \, \text{km} = 42250 \times 10^3 \, \text{m} \)
- Period \( T = 24 \, \text{hours} = 24 \times 3600 \, \text{seconds} = 86400 \, \text{seconds} \)
Calculating Orbital Speed
Now we can substitute the values into the formula:
1. **Calculate the Circumference of the Orbit:**
- \( 2\pi r = 2 \times \pi \times (42250 \times 10^3) \)
2. **Total Distance Travelled in One Revolution:**
- \( 2\pi \times 42250 \times 10^3 \approx 265,000,000 \, \text{m} \)
3. **Calculate Orbital Speed:**
- \( v = \frac{265,000,000 \, \text{m}}{86400 \, \text{s}} \approx 3070.05 \, \text{m/s} \)
4. **Converting to km/s:**
- \( v \approx 3.07 \, \text{km/s} \)
Conclusion
The calculated speed of the satellite is approximately 3.07 km/s, which matches option 'B'. Thus, the speed of the artificial satellite moving in a circular orbit of radius 42250 km taking 24 hours to revolve around the Earth is indeed:
Correct Answer: Option B - 3.07 km/s
To determine the speed of an artificial satellite in a circular orbit, we will use the formula for orbital speed, which is given by:
\[ v = \frac{2\pi r}{T} \]
where:
- \( v \) = orbital speed
- \( r \) = radius of the orbit
- \( T \) = period of revolution
Given Values
- Radius of the orbit \( r = 42250 \, \text{km} = 42250 \times 10^3 \, \text{m} \)
- Period \( T = 24 \, \text{hours} = 24 \times 3600 \, \text{seconds} = 86400 \, \text{seconds} \)
Calculating Orbital Speed
Now we can substitute the values into the formula:
1. **Calculate the Circumference of the Orbit:**
- \( 2\pi r = 2 \times \pi \times (42250 \times 10^3) \)
2. **Total Distance Travelled in One Revolution:**
- \( 2\pi \times 42250 \times 10^3 \approx 265,000,000 \, \text{m} \)
3. **Calculate Orbital Speed:**
- \( v = \frac{265,000,000 \, \text{m}}{86400 \, \text{s}} \approx 3070.05 \, \text{m/s} \)
4. **Converting to km/s:**
- \( v \approx 3.07 \, \text{km/s} \)
Conclusion
The calculated speed of the satellite is approximately 3.07 km/s, which matches option 'B'. Thus, the speed of the artificial satellite moving in a circular orbit of radius 42250 km taking 24 hours to revolve around the Earth is indeed:
Correct Answer: Option B - 3.07 km/s
Community Answer
What is the speed of an artificial satellite moving in a circular orbi...
Radius of the orbit (r): 42250 km
Time period (T): 24 hours
Convert Time Period to Seconds:
1 hour = 3600 seconds
24 hours = 24 * 3600 = 86400 second
Circumference of the Circular Orbit:
Formula: Circumference = 2 * π * radius
Substitute radius: Circumference = 2 * π * 42250 km
Value: Circumference ≈ 2 * 3.14159 * 42250 ≈ 265,458 km
Calculate Orbital Speed:
Formula: Speed = Distance / Time
Substitute values: Speed = 265,458 km / 86400 seconds
Value: Speed ≈ 3.07 km/s
The Correct Answer:
The speed of the satellite is approximately 3.07 km/s.
Hence, the correct answer is option B.
Time period (T): 24 hours
Convert Time Period to Seconds:
1 hour = 3600 seconds
24 hours = 24 * 3600 = 86400 second
Circumference of the Circular Orbit:
Formula: Circumference = 2 * π * radius
Substitute radius: Circumference = 2 * π * 42250 km
Value: Circumference ≈ 2 * 3.14159 * 42250 ≈ 265,458 km
Calculate Orbital Speed:
Formula: Speed = Distance / Time
Substitute values: Speed = 265,458 km / 86400 seconds
Value: Speed ≈ 3.07 km/s
The Correct Answer:
The speed of the satellite is approximately 3.07 km/s.
Hence, the correct answer is option B.
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What is the speed of an artificial satellite moving in a circular orbit of radius 42250 km if it takes 24 hours to revolve around the earth?a)2.98 km/sb)3.07 km/sc)3.02 km/sd)3.04 km/sCorrect answer is option 'B'. Can you explain this answer?
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