What Rotational Speed is Needed for a Satellite's 30-Minute Scan Cycle?

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SUMMARY

The discussion centers on calculating the rotational speed required for a geostationary satellite to complete a 30-minute scan cycle of the Earth's surface. The satellite, positioned 36,000 km above the Earth, must rotate to capture scanlines with a resolution of 7.5 x 7.5 km. The calculations involve determining the angle subtending the scan arc using the equation α = 2*tan-1(Resolution/R(geo)), leading to a required speed of approximately 58 rad/s to achieve the desired coverage within the specified time frame.

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  • #31
Firben said:
So if
s = rα = 36000*2*(π/180)*8.646 ≈ 10864.9 km
and the number of slices in 10865.9 is 1448.65
Thus
v = 1448.65/25 ≈ 58 km/s
Is this right ?
You're looking for an angular velocity. What units are appropriate? What units are associated with your values "1448.65" and "25"?
 
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  • #32
v = 1448.65/25 = 58 rad/s
Is this approachable ? or is I am missing something ?
 
  • #33
Firben said:
v = 1448.65/25 = 58 rad/s
Is this approachable ? or is I am missing something ?
You're almost there, but you didn't answer my last question: What units are associated with your values "1448.65" and "25"?
 
  • #34
1448.65 is km or dimensionless and 25 is minutes. I am not sure what unit i should use here
 
  • #35
Firben said:
1448.65 is km or dimensionless and 25 is minutes. I am not sure what unit i should use here
A value can't both have units of km and be dimensionless; it's a logical contradiction.

In fact, the "1448" value represents the number of slices, and one slice requires one rotation of the satellite. So an appropriate unit for it is "rotations". So your ratio is rotations/minutes, or rotations per minute, or "rpm" to use the common nomenclature.

rpm is a perfectly good unit for angular velocity, but you could also convert that to radians per second if they are looking for the answer to be expressed that way.
 
  • #36
Ok, thanks for helping me out
 

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