Kepler's Third Law allows us to find that the International Space Station (ISS) completes an orbit around Earth in 90 minutes, based on its altitude of 400 km above the Earth's surface and the radius of Earth.
To calculate how long it takes for the International Space Station (ISS) to orbit the Earth using Kepler's Third Law, we can follow specific steps detailing the process.
The ISS orbits 400 km above Earth's surface, which means the orbit's radius is the sum of Earth's radius and the altitude of the ISS: 6400 km + 400 km = 6800 km. To find the orbital period (T), since we are not given the specific value of Kepler's constant for Earth, we can use the known fact that the ISS orbits the Earth once every 90 minutes as a referencing basis.
Since Kepler's Third Law states that the square of the orbital period (T^2) is directly proportional to the cube of the semi-major axis (r^3) of the orbit, we can use the proportional relationship between the ISS orbit and any given orbit of another satellite. However, in this case, with the information that the ISS completes an orbit approximately every 90 minutes (1.5 hours), we do not need to perform further calculations.
Therefore, the period of the ISS is 90 minutes.
The probable question may be:
The ISS (International Space Station) orbits the Earth at about 400 km above the Earth's surface. The radius of Earth is about 6400 km. Use Kepler's 3rd Law and your Kepler's Constant for Earth to find and show how long it takes for the ISS to orbit the Earth in minutes: