ISS: Calculate gravity at the height of the space station

ISS: calculation of gravitational force

1. To calculate the force of gravity at the ISS you need two formulas. You need the formula for the weight: F_G= m * g * h. m is the mass of the body. g is the spatial factor on earth (9.81 N / kg). h is the height above the ground.
2. You also need the formula for the gravitational force in the radial gravitational field: F_grav= G * (m * M) / r². G is the constant of gravity (6.67 * 10^-11). m is the mass of the first body, M is the mass of the second body. r is the distance between the two bodies.
3. To calculate the force of gravity at the height of the ISS, you need the following data: Height of the space station above earth: 400 km; Earth mass: 6 * 10²⁴ kg.
4. Now set the two formulas the same: F_G= F_grav. As an expression you get: m * g * h = G * (m * M) / r
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   ². Reform the term for g: g = G * (m * M) / (r²* m * h). You can now see that you can truncate m. So the mass of the space station doesn't matter.
5. Now insert values ​​into the formula. The result is g = 8.73 N / kg. This is the acceleration due to gravity at the level of the ISS.


ISS orbit - trivia

The International Space Station ISS has been in orbit around the earth since 1998. …

Comparison of gravity on Earth and the ISS

• Compare the gravitational acceleration g on earth and at the height of the ISS. Although the space station hovers 400 km above the earth, a large part of the weight is still acting. The gravity of the ISS is 88.9% of the gravity on Earth.
• 400 km will seem high to you. If you look at the height of the ISS on a scale diagram, you will see that the space station almost scrapes above the surface of the earth. Geostationary satellites, such as those used for telecommunications, have an altitude of 36,000 km above the earth.
• Since the ISS is relatively low in altitude, it must be raised regularly so that it does not fall to earth.