Question

At some point during construction, the International Space Station had a

mass of 235,565 kg. When it orbited the Earth at an altitude of 400,000 m,
what was the approximate gravitational force on the Station due to Earth's
gravity? (Recall that Earth has a radius of 6.37 × 106 m, it has a mass of 5.97
x 1024 kg, and G = 6.67 x 10-¹1 Nm²/kg².)

Answer 1

The approximate gravitational force on the International Space Station (ISS) due to Earth's gravity is approximately 2.74 x 10^6 N.

Step-by-step explanation:

To calculate the approximate gravitational force on the International Space Station (ISS) due to Earth's gravity, we can use Newton's Law of Universal Gravitation. The formula is given by:

F = (G * m1 * m2) / r^2

Where F is the gravitational force, G is the gravitational constant (6.67 x 10^-11 Nm²/kg²), m1 and m2 are the masses of the two objects (in this case, the ISS and Earth), and r is the distance between them.

Plugging in the given values:

Mass of the ISS (m1) = 235,565 kg

Mass of Earth (m2) = 5.97 x 10^24 kg

Distance between the ISS and Earth (r) = 6.37 x 10^6 m + 4 x 10^5 m = 6.77 x 10^6 m

Using these values, the approximate gravitational force on the ISS due to Earth's gravity is:

F = (6.67 x 10^-11 Nm²/kg² * 235,565 kg * 5.97 x 10^24 kg) / (6.77 x 10^6 m)^2 ≈ 2.74 x 10^6 N

Therefore, the approximate gravitational force on the ISS due to Earth's gravity is 2.74 x 10^6 Newtons (N).