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Orbits & Escape Velocity Worksheet
By the end you will: find orbital and escape speeds, and explain why satellites stay up and what happens when they go faster or slower.
A. Explore with the simulation
For each launch height, find the speed that gives a circle, and record the time per orbit.
Launch height Speed for a circle (km/s) Time per orbit 400 km (ISS) 2,000 km 35,786 km At 400 km, launch at 7.0 km/s, then at 9.0 km/s. Describe each path.
At 400 km, raise the speed until it never comes back. What speed is that? Compare it with the circle speed.
B. Calculate (then check in the simulation)
Find the orbital speed 2,000 km above Earth. (GM = 398,600 km³/s², Earth's radius 6,371 km)
Find the escape velocity from Earth's surface.
Show that escape velocity = √2 × orbital velocity at the same radius.
Using T = 2πr ÷ v, find the ISS's period (r = 6,771 km, v = 7.67 km/s).
C. Think it through
Astronauts in the ISS float. Is gravity zero there? Explain.
Answer key (for teachers and parents)
- 400 km: 7.67 km/s, about 92 min · 2,000 km: 6.90 km/s, about 2.1 h · 35,786 km: 3.07 km/s, about 23.9 h. Higher orbits are slower and take longer.
- 7.0 km/s: too slow, it curves down and crashes. 9.0 km/s: an ellipse that reaches out to about 8,560 km above the ground and comes back.
- About 10.85 km/s, which is √2 ≈ 1.41 times the circle speed of 7.67 km/s.
- r = 8,371 km. v = √(GM ÷ r) = √(398,600 ÷ 8,371) ≈ 6.9 km/s.
- v = √(2GM ÷ R) = √(2 × 398,600 ÷ 6,371) ≈ 11.2 km/s.
- v_orbit = √(GM/r), v_escape = √(2GM/r) = √2 × √(GM/r).
- T = 2π × 6,771 ÷ 7.67 ≈ 5,550 s ≈ 92 minutes.
- No: gravity at 400 km is still about 90% of that on the ground. The station and the astronauts are falling around Earth together (free fall), so nothing presses them against the floor.
Free to print and share for teaching. Made with the interactive simulation at jugnix.com/simulations/orbits-gravity.