Centripetal Acceleration — ISS Orbit (Worked Example)

Hard

Problem

The International Space Station orbits at 7660 m/s with an orbital radius of 6.77 × 10⁶ m from Earth's centre. What is its centripetal acceleration?

Given

v = 7660 m/s
r = 6.77 × 10⁶ m

Find

Centripetal acceleration a.

Principle

Orbit is continuous free fall: the required centripetal acceleration a = v²/r is supplied entirely by gravity.

Formula

a = \frac{v^2}{r}

a = v²/r

Solution

Write the formula: $a = v^2/r$
Substitute: $a = 7660^2 / (6.77 \times 10^6)$
Numerator: $5.868 \times 10^7$
Divide: $a = 8.67\ \mathrm{m/s^2}$ toward Earth

8.67 m/s² toward Earth's centre

Unit check

(m/s)² ÷ m = m/s² — correct.

What this means physically

8.67 m/s² — about 88% of surface g. This is the local strength of gravity at ISS altitude; the station and astronauts accelerate together, which is why they float.

Common mistake

Thinking orbital acceleration is zero because velocity is constant in magnitude. Direction changes continuously — that is the acceleration.