the orbital period of the moon is 27.32 days. The international space station has an orbital period of 90 minutes. What is the mean distance between the center of the earth and the center of the international space station?
moons orbital radius: 25,201
Isn't this Kepler's Law?
Period^2=contant*radius^3
and as a ratio
PeriodISS/PeriodMoon = (radiusISS/radiusmoon)^3
change the periods to the same units, I would do hours for both, but it does not matter which you choose.
To find the mean distance between the center of the Earth and the center of the International Space Station (ISS), we can use the formula for the orbital period of an object in circular orbit:
T = 2π√(r³/GM),
where T is the orbital period, r is the distance between the centers of the two objects, G is the gravitational constant, and M is the mass of the Earth.
First, let's convert the given orbital period of the ISS from minutes to seconds:
ISS orbital period = 90 minutes = 90 * 60 = 5400 seconds.
Now, let's substitute the values into the formula:
5400 = 2π√(r³/GM).
We can rearrange the formula to solve for r:
r = (GM * (T/2π)²)^(1/3).
The mass of the Earth, M, is approximately 5.972 × 10^24 kg, and the gravitational constant, G, is approximately 6.67430 × 10^(-11) N(m/kg)².
Substituting the values:
r = (6.67430 × 10^(-11) * (5.972 × 10^24) * ((5400 / (2π))²))^(1/3).
Calculating this expression will give us the mean distance between the center of the Earth and the center of the ISS.
r = (6.67430 × 10^(-11) * 5.972 × 10^24 * ((5400 / 6.28)²))^(1/3).
r = 6,754,535 meters (approximately).
Therefore, the mean distance between the center of the Earth and the center of the International Space Station is approximately 6,754,535 meters.