Orbit Builder
Isaac Newton imagined firing a cannonball sideways from a mountain so tall it pokes out of the air. Too slow and it crashes. Fast enough and it falls all the way round the Earth forever. Can you get it into orbit?
- Speed
- 7.80 km/s
- Altitude
- 200 km
- Flight time
- 0 min
- Result
- Ready
The maths, live
Gravity g = GM ÷ r²g = 3.99×10¹⁴ ÷ (6571 km)² = 9.23 m/s²Circular orbit v = √(GM ÷ r)v = √(3.99×10¹⁴ ÷ 6571 km) = 7.79 km/sEscape v = √(2GM ÷ r)v = 11.01 km/s from 200 km upEarth and the mountain are drawn to scale and time is sped up. There is no air drag here, as if the mountain poked out above the atmosphere.
How it works
Gravity pulls the satellite towards the centre of the Earth, and the pull gets weaker further away: g = GM ÷ r². The satellite is always falling, but it is also moving sideways so fast that the curved ground drops away beneath it just as quickly as it falls.
Just above the air that takes about 7.8 km/s, and one trip round takes about an hour and a half. Go faster and the orbit stretches into an oval. At the escape speed, √(2GM ÷ r), about 11 km/s, gravity can never pull it back.
Try this
- Find the slowest launch speed that stops the satellite crashing.
- Make the mountain taller. Do you need more or less speed for a circular orbit?
- Set the speed to 10 km/s. Where in the oval does the satellite go slowest?