Can you solve it? Space
Ten problems that get harder as you go. Each has a hint and a full worked solution, but try properly before you look. Your progress is saved on this device.
- 1Hard
Moon jump
On Earth you can jump 0.5 m high. The Moon's gravity is one sixth of Earth's. Jumping with the same take-off speed, how high could you jump on the Moon, in metres?
- 2Very hard
Speed of the space station
The ISS orbits 400 km above Earth's surface (Earth's radius is about 6,400 km) and goes round once every 92 minutes. What is its speed in km/s, to 1 decimal place?
- 3Very hard
Kepler's year
A planet orbits our Sun at 4 times Earth's distance (4 AU). Using Kepler's third law, T² = a³ (T in years, a in AU), how many years does one orbit take?
- 4Hard
How long is a light-year?
Light travels at 299,792 km/s. How far does it travel in one year (365.25 days), in trillions of kilometres? Give 2 decimal places.
- 5Fiendish
Voyager to the nearest star
Proxima Centauri is 4.24 light-years away (1 light-year ≈ 9.46 × 10¹² km). Voyager 1 travels at about 17 km/s. Roughly how many thousand years would it take to get there?
- 6Fiendish
Escaping a bigger planet
Earth's escape velocity is 11.2 km/s. A planet has the same density as Earth but twice the radius. What is its escape velocity in km/s? (v = √(2GM/R).)
- 7Very hard
The perfect eclipse
The Sun and the Moon look almost exactly the same size in our sky, but the Sun is about 400 times farther away. The Moon is about 3,500 km across. About how many million kilometres across is the Sun?
- 8Very hard
Sols in a Martian year
A Mars year lasts 687 Earth days. A Mars day, called a sol, lasts 24 hours 37 minutes. How many sols are in a Martian year, to the nearest whole number?
- 9Hard
Calling Mars
At its closest, Mars is about 54.6 million km from Earth. Radio waves travel at 300,000 km/s. How many minutes does a message take to reach Mars? Give 1 decimal place.
- 10Fiendish
Would Saturn float?
Saturn's mass is 5.68 × 10²⁶ kg and its radius is 58,200 km. What is its average density in g/cm³, to 2 decimal places? (Water is 1 g/cm³.)