The global positioning system (GPS) satellite that moves in a circular orbit with period of 11h 58 min has an orbital radius of: 26.55465166*10^6 m
To solve this problem the orbital radius formula and the procedure we will use is:
r =[tex]\sqrt[3][/tex][tex]\sqrt[3]{}[/tex][(G* m *T²)/(4 * π²)]
Where:
- r = orbital radius
- G = Gravitational constant
- m = Mass of the Earth
- T = Time period of the satellite
- π = mathematical constant
Information about the problem:
- T = 11h 58 min
- G = 6.67 × 10⁻¹¹ m³/kgs²
- m= 5.972 × 10²⁴ kg
- π = 3.1416
- r =?
By converting the time period of (h) and (min) from (s) we have:
T = (11h *3600 s/ 1 h) + (58 min * 60 s/1 min)
T = 39600 s +3480 s
T = 43080 s
Applying the orbital radius formula we get:
r =[tex]\sqrt[3][/tex][tex]\sqrt[3]{}[/tex][(G* m *T²)/(4 * π²)]
r =[tex]\sqrt[3][/tex][tex]\sqrt[3]{}[/tex][(6.67 × 10⁻¹¹ m³/kgs² * 5.972 × 10²⁴ kg *(43080 s)²)/(4 * (3.1416)²)]
r =[tex]\sqrt[3][/tex][tex]\sqrt[3]{}[/tex][1.8725*10^22 m³]
r= 26.55465166*10^6 m
What is the orbital radius?
It is the maximum of the radial distribution curve of the outermost orbital.
Learn more about orbital radius at: brainly.com/question/14437688
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