Satellites and Circular Orbits

Falling around the world

The International Space Station circles Earth about every 93 minutes, at a speed of nearly 7.7 km/s. Canadian astronauts such as Chris Hadfield and David Saint-Jacques have lived on it for months, floating in the cabin. In April 2026, Canadian Space Agency astronaut Jeremy Hansen flew around the Moon on Artemis II, the first crewed lunar mission since Apollo, splashing down on April 10, 2026. Every one of those trips is planned with the physics in this lesson.

Remember from the Dynamics unit: an object moving in a circle of radius r at constant speed v has a centripetal acceleration a_c = v²/r = 4π²r/T² toward the centre, and it needs a net force F_c = mv²/r toward the centre. For a satellite, that force is gravity.

Newton's cannon

Newton imagined a cannon on a very tall mountain, above the air, firing horizontally.

• A slow cannonball curves down and lands nearby (A).
• A faster one lands farther away (B, C).
• Earth's surface curves away beneath a moving object: over a horizontal distance of 7.9 km, the ground drops about 4.9 m below a straight line. A ball launched horizontally falls 4.9 m in its first second. So if it moves at about 7.9 km/s (just above the surface, ignoring air), the ground curves away exactly as fast as the ball falls. It keeps falling and keeps missing the ground. It is in orbit (D).

So an orbit is not an escape from gravity. It is free fall with enough sideways speed.

The orbit equations

For a satellite of mass m in a circular orbit of radius r around a planet of mass M, gravity provides the centripetal force:

GMm/r² = mv²/r

Cancel m and one r:

v = √(GM/r)

The time for one orbit is the circumference divided by the speed, T = 2πr/v. Substituting v:

T = 2π√(r³/GM), or equivalently T² = (4π²/GM) r³

Three things to notice:

1. The satellite's mass m cancels. A wrench and a space station at the same r orbit at the same speed. That is why a tool let go during a spacewalk drifts alongside the astronaut.
2. Lower orbits are faster. Smaller r gives larger v and shorter T.
3. For a given planet, r fixes everything: choosing an orbit radius fixes its speed and period.

Apparent weightlessness

On the ISS, g is still 8.6 N/kg. So why do astronauts float?

Your weight is the gravitational force on you. What you feel as weight is the normal force: the floor pushing up on you. On the ISS, the astronaut, the floor and the whole station are all falling toward Earth with the same acceleration (all at g = 8.6 m/s²). The floor never has to push the astronaut, so the normal force is zero. The astronaut feels weightless, even though gravity is pulling on them with about 88% of their Earth weight. This is apparent weightlessness.

You get the same feeling for a moment at the top of a drop ride, or when an elevator starts down quickly. Long stays in apparent weightlessness weaken bones and muscles, which is why astronauts exercise about two hours a day.

Orbits Canada uses

• Low Earth orbit: the ISS (about 400 to 420 km), where Canada's robotic arm Canadarm2 works, and the three RADARSAT Constellation Mission satellites (about 600 km, launched in 2019), which use radar to monitor sea ice, ships, floods and land.
• Medium Earth orbit: the GPS constellation, about 31 operational satellites (the exact count changes as new ones launch and old ones retire) in six orbital planes about 20 200 km up, each circling Earth twice a day.
• Geostationary orbit: TV, internet and weather satellites over the equator. From southern Canada they sit in the southern sky. In the far North they are low on the horizon or below it, which makes satellite service there harder.

You will look at how satellites affect society and the environment in the lesson Fields, Technology and Society.