Final answer:
The ISS orbits the Earth at an altitude of 400 km with an orbital speed calculated using the formula v = √(G · M / r). Given the Earth's mass and radius, plus the altitude of the ISS, the orbital speed is approximately 7.67 km/s, allowing the ISS to circle the Earth every 90 minutes.
Step-by-step explanation:
The International Space Station (ISS) orbits the Earth at an altitude of approximately 250 miles (400 kilometers) above the Earth's surface. To calculate the ISS's orbital speed, we can use the formula for the gravitational force that keeps it in orbit: F = (G · M · m) / r^2, where G is the gravitational constant, M is the mass of the Earth, m is the mass of the ISS, and r is the distance from the center of the Earth to the ISS.
However, since we're interested in the orbital speed, we'll use a different formula derived from this force equation called the orbital velocity formula: v = √(G · M / r). Given the Earth's mass is 5.98 X 10^24 kilograms and its radius is 6.37 X 10^6 meters, we add the 400 km (400,000 meters) to the radius to account for the altitude of the ISS. This gives us an orbital radius r of 6.77 X 10^6 meters. Using these values, we can calculate the ISS's orbital speed.
The calculation yields an orbital speed of approximately 7.67 kilometers per second. This calculation shows that the ISS travels at a high speed to maintain its orbit, circling the Earth roughly every 90 minutes. This frequency also provides opportunities for astronauts to capture stunning photographs showing that the Earth is round from every perspective.