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A geo-stationary satellite orbits around the earth in a circular orbit of radius 36,000km. Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface (Rearth = 6,400km) will approximately be
- a)1/2 hr
- b)1 hr
- c)2 hr
- d)4 hr
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A geo-stationary satellite orbits around the earth in a circular orbit...
Note : A satellite revolving near the earth's surface has a time period of 84.6 min.
We know that as the height increases, the time period increases. Thus the time period of the spy satellite should be slightly greater than 84.6 minutes.
We know that as the height increases, the time period increases. Thus the time period of the spy satellite should be slightly greater than 84.6 minutes.
∴ Ts = 2 hr
Most Upvoted Answer
A geo-stationary satellite orbits around the earth in a circular orbit...
Explanation:
In order to understand why the time period of the spy satellite is approximately 2 hours, we need to consider the relationship between the time period and the radius of the orbit.
1. Time Period of a Satellite:
The time period of a satellite is the time it takes for the satellite to complete one full orbit around the Earth. It can be calculated using the following formula:
T = 2π√(r^3/GM)
Where:
T = Time period of the satellite
r = Radius of the satellite's orbit
G = Universal gravitational constant
M = Mass of the Earth
2. Geostationary Satellite:
A geostationary satellite is located in a circular orbit directly above the Earth's equator. It remains stationary relative to a fixed point on the Earth's surface because its orbital period is exactly equal to the Earth's rotational period. In this case, the radius of the orbit is 36,000 km.
3. Spy Satellite:
The spy satellite orbits a few hundred kilometers above the Earth's surface. Let's assume the radius of its orbit is r' km.
4. Comparison:
To compare the time periods of the geostationary satellite and the spy satellite, we can use the formula mentioned earlier:
T = 2π√(r^3/GM)
For the geostationary satellite, r = 36,000 km.
For the spy satellite, r' = 6400 km + a few hundred km.
Since the radius of the spy satellite's orbit is much smaller than the radius of the geostationary satellite's orbit, we can approximate the time period using the formula:
T' = 2π√(r'^3/GM)
Substituting the values:
T' = 2π√((6400 + a few hundred)^3/GM)
Since the value of a few hundred km is very small compared to 6400 km, we can neglect it in the equation:
T' ≈ 2π√((6400)^3/GM)
5. Conclusion:
From the approximation, we can see that the time period of the spy satellite is approximately the same as the time period of a satellite in a circular orbit of radius 6400 km. This is because the small increase in radius does not significantly affect the time period. Therefore, the time period of the spy satellite is approximately 2 hours. Hence, the correct answer is option 'C'.
In order to understand why the time period of the spy satellite is approximately 2 hours, we need to consider the relationship between the time period and the radius of the orbit.
1. Time Period of a Satellite:
The time period of a satellite is the time it takes for the satellite to complete one full orbit around the Earth. It can be calculated using the following formula:
T = 2π√(r^3/GM)
Where:
T = Time period of the satellite
r = Radius of the satellite's orbit
G = Universal gravitational constant
M = Mass of the Earth
2. Geostationary Satellite:
A geostationary satellite is located in a circular orbit directly above the Earth's equator. It remains stationary relative to a fixed point on the Earth's surface because its orbital period is exactly equal to the Earth's rotational period. In this case, the radius of the orbit is 36,000 km.
3. Spy Satellite:
The spy satellite orbits a few hundred kilometers above the Earth's surface. Let's assume the radius of its orbit is r' km.
4. Comparison:
To compare the time periods of the geostationary satellite and the spy satellite, we can use the formula mentioned earlier:
T = 2π√(r^3/GM)
For the geostationary satellite, r = 36,000 km.
For the spy satellite, r' = 6400 km + a few hundred km.
Since the radius of the spy satellite's orbit is much smaller than the radius of the geostationary satellite's orbit, we can approximate the time period using the formula:
T' = 2π√(r'^3/GM)
Substituting the values:
T' = 2π√((6400 + a few hundred)^3/GM)
Since the value of a few hundred km is very small compared to 6400 km, we can neglect it in the equation:
T' ≈ 2π√((6400)^3/GM)
5. Conclusion:
From the approximation, we can see that the time period of the spy satellite is approximately the same as the time period of a satellite in a circular orbit of radius 6400 km. This is because the small increase in radius does not significantly affect the time period. Therefore, the time period of the spy satellite is approximately 2 hours. Hence, the correct answer is option 'C'.
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A geo-stationary satellite orbits around the earth in a circular orbit of radius 36,000km. Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface (Rearth = 6,400km) will approximately bea)1/2 hrb)1 hrc)2 hrd)4 hrCorrect answer is option 'C'. Can you explain this answer?
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