Orbits and Escape Velocity
How fast must you throw something so it never comes down? Fire Newton's cannon from high above Earth and slide the speed: crash, circle, stretch into an ellipse, or escape forever.
Class 11 Gravitation● circle at 7.67 km/s● escape at 10.85 km/s
Try this
0 of 5 doneFire too slowly and watch the cannonball fall back to Earth.Hint: any speed below about 7 km/s at ISS height
Find the speed for a perfect circle at the ISS's height.Hint: watch for the dashed ring. It's between 7 and 8 km/s
Make a stretched orbit that swings out 3 times farther than where it started.Hint: go faster than a circle, but not fast enough to escape
Escape Earth's gravity forever!Hint: you need about √2 times the circle speed
Park a satellite in geostationary orbit: exactly one trip a day.Hint: pick the 35,786 km height and find its circle speed
What's happening
An orbit is falling and missing
Gravity pulls the cannonball toward Earth's centre all the time. Fire it slowly and it curves into the ground. Fire it faster and the ground curves away beneath it just as fast as it falls, so it keeps falling round and round. That's all an orbit is, and why astronauts float: they are falling too.
The speed for a circle
For a circular orbit, gravity must supply exactly the pull needed to bend the path into a circle. Farther from Earth, gravity is weaker, so a circle needs less speed and each lap takes longer. Near the ground that speed is about 7.9 km/s, roughly 28,000 km/h.
Escape velocity
Go faster than a circle and the orbit stretches into an ellipse that swings out far and comes back slower. At √2 times the circle speed the ellipse never closes: the object escapes and never returns. From Earth's surface this is about 11.2 km/s.
Who figured this out?
Johannes Kepler
1609–1619, GermanyFound from careful observations that planets move in ellipses, move faster when closer to the Sun, and that bigger orbits take longer (T² ∝ a³).
Isaac Newton
1687, EnglandImagined a cannon on a very tall mountain: fire fast enough and the ball falls round Earth forever. His law of gravity explained why Kepler's laws work.
Yuri Gagarin
1961, Soviet UnionThe first person to orbit Earth. His flight on Vostok 1 took 108 minutes.
Learn more
- Orbits and Kepler's laws · NASA Science
- International Space Station · NASA
- Mars Orbiter Mission (Mangalyaan) · ISRO
- Newton's cannonball · Wikipedia
- Escape velocity · Wikipedia
Check yourself
1. Why doesn't the International Space Station fall down to Earth?
2. Escape velocity is how many times the circular orbit speed at the same height?
3. Does a heavier rocket need a higher escape velocity?
4. A satellite moves to a higher circular orbit. What happens?
Common questions
What is escape velocity?
Escape velocity is the minimum speed an object needs to break free from a planet's gravity without any further push. It is ve = √(2GM/R). For Earth, from the surface, it is about 11.2 km/s, roughly 40,000 km/h. It does not depend on the mass of the object.
What is orbital velocity?
Orbital velocity is the speed needed to stay in a circular orbit at a given distance r from the planet's centre: vo = √(GM/r). Close to Earth's surface it is about 7.9 km/s. Higher up it is smaller: the ISS at 400 km moves at about 7.7 km/s.
What is the relation between escape velocity and orbital velocity?
At the same distance from the planet, escape velocity is √2 (about 1.414) times the circular orbital velocity: ve = √2 × vo. Near Earth's surface, 7.9 km/s × 1.414 ≈ 11.2 km/s.
What is a geostationary orbit?
A geostationary orbit is a circular orbit about 35,786 km above the Equator, where a satellite takes exactly one day to go round, matching Earth's spin. So it seems to hang still over one place. India's INSAT and GSAT communication and weather satellites use it.
What are Kepler's laws of planetary motion?
First, orbits are ellipses with the planet (or Sun) at one focus. Second, a line from the planet to the orbiting body sweeps out equal areas in equal times, so it moves fastest when closest. Third, the square of the orbit time is proportional to the cube of the orbit's size: T² ∝ a³.
Why do astronauts feel weightless in orbit?
Not because there is no gravity: at the ISS's height gravity is still about 90% of its strength on the ground. Astronauts and their spacecraft are falling around Earth together at the same rate, so nothing presses on anything. This is called free fall.
Earth to scale; no air and no Moon. Real rockets don't get one push: they burn for several minutes, but the speeds they must reach are the ones shown here.
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