Question

The International Space Station (ISS) is a space station orbiting the earth above the ground. If the radius of the earth is 3,958.8 miles, mass of earth is 5.972 x 10 24 kg, the period of the ISS at the orbit around the earth is 7.84 hours, can you calculate what is the distance from the ISS to the surface of the earth, in unit of miles

Answer 1

The International Space Station orbits the Earth approximately 248.5 miles above its surface. By adding the Earth's radius and the ISS's orbit altitude, we find the distance from the center of the Earth to the ISS is 4,207.3 miles.

Step-by-step explanation:

To calculate the distance from the International Space Station (ISS) to the surface of Earth, we must consider both the Earth's radius and the height at which the ISS orbits. Given that the Earth's radius is 3,958.8 miles and the ISS orbits approximately 400 kilometers (about 248.5 miles) above Earth's surface, we simply add these two numbers together to find the distance from the center of the Earth to the ISS.

The Earth's radius is 3,958.8 miles, and the ISS orbit altitude is 248.5 miles, so:

• Distance from ISS to Earth's surface = Earth's radius + ISS orbit altitude
• Distance from ISS to Earth's surface = 3,958.8 miles + 248.5 miles
• Distance from ISS to Earth's surface = 4,207.3 miles

Therefore, the ISS is 4,207.3 miles from the center of the Earth, which means it is about 248.5 miles above the Earth's surface.

Answer 2

8488 miles

Step-by-step explanation:

The orbital period around an earth is given as:

`T=2\pi \sqrt{(r^3)/(Gm) }`

Where G = constant = 6.67 x 10ˉ¹¹ N m² kgˉ², m = mass of object, T = period taken to round the earth, r = distance from the center of the earth to the orbiting object = radius of earth + orbital altitude.

Given that T = 7.84 hours = 28224 seconds, m = 5.972 x 10²⁴ kg, radius of earth = 3,958.8 miles = 6371071 m

`T=2\pi \sqrt{(r^3)/(Gm) }\\\\squaring:\\\\T^2=4\pi^2 ((r^3)/(Gm) )\\\\r^3=(GmT^2)/(4\pi^2) \\\\r=\sqrt[3]{(GmT^2)/(4\pi^2) } \\\\r=\sqrt[3]{(6.67*10^(-11)*5.972*10^(24)*(28224)^2)/(4\pi^2) } \\\\r=20031232.62\ meters`

r = radius of earth + distance from the ISS to the surface of the earth

distance from the ISS to the surface of the earth = r - radius of earth

distance from the ISS to the surface of the earth = 20031232.62 meters - 6371071 meters = 13660161.62 meters

distance from the ISS to the surface of the earth = 13660161.62 meters = 8488 miles