The International Space Station stays in orbit because it is constantly falling around Earth, not because gravity is absent. At its altitude of about 400 km, gravity is still strong enough to provide the centripetal acceleration needed for circular motion. The ISS moves sideways at about 7.7 km/s, so as it falls, Earth curves away beneath it.
This balance makes orbit possible, but the orbit is not perfectly permanent.
Key Facts
- Circular orbit speed: v = sqrt(GM/r)
- Centripetal acceleration in orbit: a = v^2/r
- Gravity provides the inward force: GMm/r^2 = mv^2/r
- Drag force model: Fd = 1/2 rho v^2 Cd A
- Orbital period of the ISS is about 90 minutes.
- Reboosts add velocity, raising the ISS to a higher orbit and replacing energy lost to drag.
Vocabulary
- Low Earth orbit
- A region of orbit close to Earth, usually between about 160 km and 2,000 km above the surface.
- Atmospheric drag
- A resistive force caused by thin air molecules hitting a spacecraft and slowing it down.
- Reboost
- A planned engine burn that increases a spacecraft's speed and raises its orbit.
- Orbital velocity
- The sideways speed an object needs to keep falling around Earth instead of falling straight down.
- Centripetal acceleration
- The inward acceleration that keeps an object moving along a curved or circular path.
Common Mistakes to Avoid
- Saying there is no gravity on the ISS, which is wrong because gravity at ISS altitude is still about 90% as strong as at Earth's surface.
- Thinking the ISS stays up because it is outside the atmosphere, which is wrong because there is still very thin air in low Earth orbit that causes drag.
- Assuming a reboost pushes the ISS straight upward, which is wrong because spacecraft usually fire engines mostly along the direction of motion to increase orbital energy.
- Using Earth's surface radius as the orbital radius without adding altitude, which is wrong because orbit formulas require distance from Earth's center, not height above the ground.
Practice Questions
- 1 The ISS orbits at an altitude of 400 km. Using Earth's radius 6.37 x 10^6 m and GM = 3.99 x 10^14 m^3/s^2, calculate its circular orbital speed using v = sqrt(GM/r).
- 2 If a small reboost changes the ISS speed by 2.0 m/s and the ISS mass is 4.2 x 10^5 kg, estimate the impulse delivered using J = m delta v.
- 3 Explain why atmospheric drag makes the ISS lose altitude over time, and why firing engines in the direction of motion can raise its orbit.