Physics · Class 11

Test the escape-energy threshold

Escape occurs when the launch kinetic energy cancels or exceeds the negative gravitational potential energy. The escape speed depends on the central body and launch radius but not the probe mass.

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Test the escape-energy threshold

விடுபடு வேகம் பொருளின் நிறையைப் பொறுத்ததல்ல. இயக்க ஆற்றல் ஈர்ப்பு நிலை ஆற்றலின் அளவை ஈடுகட்ட வேண்டும்.

Key notes, relationships and model limits

Key relationship

vesc=√(2GM/r); ε=½v²−GM/r; bound radial turning point rmax=−GM/ε.

Remember

Escape occurs when the launch kinetic energy cancels or exceeds the negative gravitational potential energy. The escape speed depends on the central body and launch radius but not the probe mass.

Common trap

Escape speed is not a continuously required cruising speed.

Model limits

Radial launch outside Earth; no air resistance, rotation or thrust after launch. Exact zero total energy gives marginal escape with zero speed at infinity.

What you will learn

Use total energy to distinguish bound launch, marginal escape and unbound launch.

Try the experiment

Try both scenarios, change one control, and predict the result before checking the graph and readouts.

Think of it this way

Change one input while keeping the others fixed, as you would in a controlled experiment.

Worked example

At Earth radius, vesc≈11.19 km/s. At four times that radius, escape speed halves to about 5.59 km/s.

Why this matters

The model connects test the escape-energy threshold with an observable reading. Check the equation and assumptions before applying it.

Before you start

SI units · algebra · graph reading

Check your understanding

What happens when launch speed equals escape speed?

It immediately falls back to the launch point
The probe reaches infinity with zero limiting speed
It reaches infinity still at its launch speed

Read the explanation

At escape threshold ε=0, so no energy remains as kinetic energy at infinite radius.

Course connection: Class XI Chapter 7. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.