Module 2 · Falling around: orbits
Practice: predict the path
Predict the path
For each case, say what the Earth does next. Hints are optional and revealed one at a time.
Toolbox
- Rule 1: With no force a body moves in a straight line at constant speed.
- Rule 2: Gravity pulls toward the Sun. The sideways speed decides whether the body misses it.
- Rule 3: Escape velocity is the square root of 2 times the circular orbital speed.
Hints, feedback and the worked solution need JavaScript. The tasks are listed below.
Challenge 1 Level 1: Guided
The Sun suddenly disappears. What does the Earth do?
What force is left acting on the Earth?No force means constant velocity.With no Sun there is no force to bend the path. By Newton's first law the Earth keeps its velocity, about 29.8 km/s, and moves in a straight line.Challenge 2 Level 2: Supported
The Earth's sideways speed is cut to half. What happens?
Below the circular speed gravity pulls harder than the sideways motion can carry the Earth past.The circular speed balances gravity at that distance. At half of it the Earth falls inward on an ellipse whose far point is the current distance, and in the course's model it plunges toward the Sun.Challenge 3 Level 3: Independent
The Earth's speed is raised to 1.5 times the circular speed. Is that enough to escape? Use the factor from rule 3.
Escape needs about 1.41 times the circular speed.Escape speed is the square root of 2, about 1.41, times the circular speed. 1.5 is above that, so the path is open: the Earth leaves and does not return.