I have a question about the International Space Station-Its been orbiting earth at 350km-If the radius of the earth is 6,370 km, what is the period of orbit for the Space Station?

Secondly, if it was moved to a geosynchronous orbit, what would the new altitude of the station be?

If youcould just direct me or give me a clue how to solve these, I would appreciate it. I think something is missing from these questions in order to solve them. If you could even verify that, I'd appreciate it

Thank you

No, you have all you need.

consider centripetal force, that has to equal gravity.

GMe*m/(re+h)^2=m w^2(re+h)

w= Find w. Then, w=2PI/Period, solve for period.

For the geosynchronous orbit, you know period, find angular veloicty in radians/sec, and then find h.

Thank you-I'll try it and get back with a possible answer maybe tomorrow

To find the period of orbit for the International Space Station (ISS), you can use Kepler's Third Law. Kepler's Third Law states that the square of the period of an object's orbit is proportional to the cube of its average distance from the center of mass of the object it is orbiting.

Given that the ISS orbits at an altitude of 350 km above the Earth's surface, we need to find the total distance from the center of the Earth to the ISS's orbit.

The radius of the Earth is given as 6,370 km. So the average distance from the center of the Earth to the ISS's orbit would be the sum of the Earth's radius and the ISS's altitude:

Average distance = Earth's radius + ISS's altitude
Average distance = 6,370 km + 350 km

To find the period, we can use the following equation:

Period^2 = (Average distance)^3

Now, substitute the average distance calculated above into the equation:

Period^2 = (6770 km)^3

To solve for the period, we need to take the square root of both sides of the equation:

Period = square root of [(6,770 km)^3]

Calculating this will give you the period of orbit for the ISS.

Now, let's move on to the second part of the question about moving the ISS to a geosynchronous orbit. In a geosynchronous orbit, the satellite (in this case, the ISS) orbits the Earth at the same rate at which the Earth rotates, so it appears to be stationary from the ground.

To determine the new altitude of the ISS in a geosynchronous orbit, we need to calculate the distance from the center of the Earth to that orbit. This distance is equal to the radius of the Earth plus the distance from the Earth's surface to the geosynchronous orbit.

In order to provide a more precise answer, we need to know the exact height of a geosynchronous orbit. Generally, geosynchronous orbit is about 35,786 km above the Earth's surface. So, the new altitude of the ISS in a geosynchronous orbit would be:

New altitude = Earth's radius + Geosynchronous orbit altitude
New altitude = 6,370 km + 35,786 km

Adding these values will give you the new altitude of the ISS in a geosynchronous orbit.

Please note that the exact altitude of a geosynchronous orbit can vary depending on specific requirements (e.g., communications satellites might be at a slightly different altitude).