Question

The international Space Station (ISS) orbits the Earth once every 90 mins at an altitude of 409 km. How high would it have to be in order to be to be in geosynchronous orbit

Answer 1

It would have to be 36,719 Km high in order to be to be in geosynchronous orbit.

To find the answer, we need to know about the third law of Kepler.

What's the Kepler's third law?

• It states that the square of the time period of orbiting planet or satellite is directly proportional to the cube of the radius of the orbit.
• Mathematically, T²∝a³

What's the radius of geosynchronous orbit, if the time period and altitude of ISS are 90 minutes and 409 km respectively?

• The time period of geosynchronous orbit is 24 hours or 1440 minutes.
• As the Earth's radius is 6371 Km, so radius of the ISS orbit= 6371km + 409 km = 6780km.
• If T1 and T2 are time period of geosynchronous orbit and ISS orbit respectively, a1 and a2 are radius of geosynchronous orbit and ISS orbit, as per third law of Kepler, (T1/T2)² = (a1/a2)³
• a1= (T1/T2)⅔×a2

           = (1440/90)⅔×6780

           = 43,090 km

• Altitude of geosynchronous orbit = 43,090 - 6371= 36,719 km

Thus, we can conclude that the altitude of geosynchronous orbit is 36,719km.

Learn more about the Kepler's third law here:

brainly.com/question/16705471

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