Question

The International Space Station has a circular orbit about the Earth that has a period of 91.5 minutes. Determine its speed, orbital radius, altitude and acceleration if the mass of the Earth is 6 x 10 24 kg. (r= 1300 km, v=1.49 km/s, a=1.7 m/s 2, altitude = 1300km-r earth assuming space station has negligible radius

Answer 1

The speed of the International Space Station is approximately 1.49 km/s. Its orbital radius is approximately 1300 km + 6.37 x
`10^6` m. The altitude is approximately 1300 km - 6.37 x
`10^6` m.

To determine the speed, orbital radius, altitude, and acceleration of the International Space Station (ISS), we can use the formulas for circular motion and gravitational force.

1. First, let's calculate the speed (v) of the ISS. The formula for the speed of an object in circular motion is v = 2πr / T, where r is the radius of the orbit and T is the period of the orbit. Plugging in the given values, we have v = (2π)(1300 km) / 91.5 min. Converting the period to seconds (91.5 min * 60 s/min), we find v = 1.49 km/s.
2. Next, let's find the orbital radius (r) of the ISS. The orbital radius is the distance from the center of the Earth to the center of the ISS's orbit. This can be calculated by subtracting the radius of the Earth (6.37 x
   `10^6` m) from the altitude of the ISS (1300 km). So, the orbital radius is (1300 km + 6.37 x
   `10^6` m).
3. Now, let's calculate the altitude of the ISS. The altitude is the distance from the surface of the Earth to the position of the ISS. This can be calculated by subtracting the radius of the Earth (6.37 x
   `10^6` m) from the orbital radius.
4. Finally, let's find the acceleration (a) of the ISS. The acceleration is caused by the force of gravity between the ISS and the Earth. The formula for the centripetal acceleration is a =
   `v^2` / r. Plugging in the values for speed and orbital radius, we have a =
   `(1.49 km/s)^2` / (1300 km + 6.37 x
   `10^6` m).

Calculating these values, we find that the speed of the ISS is approximately 1.49 km/s, the orbital radius is approximately 1300 km + 6.37 x
`10^6` m, the altitude is approximately 1300 km - 6.37 x
`10^6` m, and the acceleration is approximately 1.7
`m/s^2`.