What is the period of the ISS orbit?

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SUMMARY

The period of the International Space Station (ISS) orbit is calculated using the formula T^2/R^3 = (4π^2)/(GM), where G is the gravitational constant (6.67x10^-11 N*m^2/kg^2) and M is the mass of the Earth (5.98x10^24 kg). The correct orbital period is approximately 91.3 minutes, not the incorrectly calculated 1.1 seconds. The radius R must include the Earth's radius (approximately 6.37x10^6 m) added to the ISS altitude of 347 km (or 347,000 m), resulting in a total radius of 6.72x10^6 m.

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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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