What is the period of the ISS orbit?

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The International Space Station (ISS) orbits Earth at an altitude of 347 km, requiring calculations to determine its orbital period. The correct formula to use is T^2/R^3 = (4Pi^2)/(GM), where 'R' must include the Earth's radius plus the altitude of the ISS. A common mistake is using only the altitude, which leads to incorrect results, such as 1.1 seconds instead of the correct period of 91.3 minutes. The proper distance 'R' is the sum of the Earth's radius (approximately 6,371 km) and the ISS's altitude, totaling about 6,718 km. Accurate calculations are essential for determining the orbital period of the ISS.
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Homework Statement


The International Space Station (ISS) circles the Earth at an altitude of 347 km.
What is the period of the orbit of the ISS expressed in minutes?
G=6.67x10^-11 N * m^2 /kg^2
M(Earth)=5.98*10^24 kg

Homework Equations


T^2/R^3 = (4Pi^2)/(GM)
So: T^2= Sqrt(((4Pi^2)/(GM))*(r^3))

The Attempt at a Solution


Alright, so I've been plugging in these numbers for awhile, and I keep getting the wrong answer: 1.1 seconds. The right answer is 91.3 min.
T is in seconds when initially calculated, right? I'm still doing something wrong, but I'm hoping to just double check on that.
 
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KCEWMG said:

Homework Statement


The International Space Station (ISS) circles the Earth at an altitude of 347 km.
What is the period of the orbit of the ISS expressed in minutes?
G=6.67x10^-11 N * m^2 /kg^2
M(Earth)=5.98*10^24 kg

Homework Equations


T^2/R^3 = (4Pi^2)/(GM)
So: T^2= Sqrt(((4Pi^2)/(GM))*(r^3))

The Attempt at a Solution


Alright, so I've been plugging in these numbers for awhile, and I keep getting the wrong answer: 1.1 seconds. The right answer is 91.3 min.
T is in seconds when initially calculated, right? I'm still doing something wrong, but I'm hoping to just double check on that.

I'm not sure what numbers you're plugging in, but keep in mind that the 'R' in Newton's law of gravitation is the distance between the centres of mass of the two bodies. What is the distance between the ISS and the centre of mass of the Earth? Hint: it is not 347 km.
 
Ahh, 347000 m + 6.37x10^6 m! Perfect, thanks!
 

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