A body thrown horizontally so that it never reaches the ground can circle the Earth. The speed required near the surface is called the first cosmic speed: gravity acts as the centripetal force, mg = mυ²/R, so υ₁² = gR and υ₁ ≈ 7.9 km/s. At a greater height (say 300 km) the required speed is slightly less, about 7.7 km/s. A man-made body placed in orbit around the Earth is an artificial satellite; to avoid air resistance it flies several hundred kilometres up. At 11.2 km/s (second cosmic speed) a body leaves the Earth’s neighbourhood, and at 16.7 km/s (third cosmic speed) it leaves the Solar System. The first artificial satellite was launched on 4 October 1957, and on 12 April 1961 Yuri Gagarin became the first person in space.
Worked examples
υ₁² = gR = 9.8 · 6.4 · 10⁶ ≈ 63 · 10⁶ m²/s²; since 7.9 · 7.9 ≈ 63, υ₁ ≈ 7.9 · 10³ m/s = 7.9 km/s.
At 7.9 km/s in one hour: 7.9 · 3600 ≈ 28 400 km; the Earth’s circumference is about 40 000 km, so one orbit takes roughly 85–90 minutes.
Class activity
“What do satellites give us?”: the class lists satellite uses: communication, weather, navigation, Earth observation. Safety: never experiment with rockets or explosives.
Practice
1
What is the first cosmic speed and its value?
The speed needed to orbit near the Earth’s surface, about 7.9 km/s.
2
Why do satellites fly at several hundred kilometres?
Because the air there is very thin, so air resistance is almost absent.
3
At 8 km/s, how many km does a satellite cover in 100 s?
800
4
Why doesn't a satellite fall to the Earth although it is in orbit?
It is falling, but its horizontal speed is so large that the Earth’s surface curves away; gravity just bends its path into a circle.