What is the period of the ISS orbit?

In summary, the International Space Station (ISS) orbits the Earth at an altitude of 347 km. Using Newton's law of gravitation, the period of its orbit can be calculated using the equation T^2/R^3 = (4Pi^2)/(GM), where T is the period in seconds, R is the distance between the centres of mass of the ISS and Earth, G is the gravitational constant, and M is the mass of the Earth. The correct answer is 91.3 minutes.
  • #1
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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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  • #2
Welcome to PF, :smile:

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.
 
  • #3
Ahh, 347000 m + 6.37x10^6 m! Perfect, thanks!
 

1. What is the formula for calculating the orbit of an object given its radius?

The formula for calculating the orbit of an object given its radius is 2πr, where r is the radius of the orbit.

2. How do I find the radius of an orbit given its period?

To find the radius of an orbit given its period, you can use the formula r = (G*M*T^2)/(4π^2), where G is the gravitational constant, M is the mass of the central body, and T is the period of the orbit.

3. Can the radius of an orbit change over time?

Yes, the radius of an orbit can change over time due to various factors such as gravitational pull from other objects, atmospheric drag, or changes in the mass of the central body.

4. How does the radius of an orbit affect the speed of an object?

The radius of an orbit and the speed of an object are inversely proportional. This means that as the radius of the orbit increases, the speed of the object decreases, and vice versa. This relationship is described by v = √(G*M/r), where v is the speed of the object, G is the gravitational constant, M is the mass of the central body, and r is the radius of the orbit.

5. How does the radius of an orbit affect the stability of an object?

The stability of an object in orbit is affected by the radius of its orbit. Objects in smaller orbits have a higher velocity and are more likely to escape the orbit, while objects in larger orbits have a lower velocity and are more likely to remain in the orbit. Therefore, the radius of an orbit can impact the stability of an object in that orbit.

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