Gravitation

Physics · Class 11

Simulation · Physics · Class 11

Equal areas in equal times

"Equal areas in equal times" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the NCERT section "The law of areas" in Gravitation. A planet on an ellipse sweeps shaded sectors in equal time intervals; speed and KE at each point; v_P/v_A = r_A/r_P. NEET has asked about this idea 2 times in 10 years of papers. JEE Main asked 39 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).

From the lesson The law of areas in Gravitation. Change the values and watch what happens.

Equal areas in equal timesPhysics · Class 11

What it shows

NCERT §7.2

A planet on an ellipse sweeps shaded sectors in equal time intervals; speed and KE at each point; v_P/v_A = r_A/r_P.

Controls

3 to try

  • Slidereccentricity 0–0.8
  • Slidertime step for sectors
  • Dragplanet position marker

Try this

Set the eccentricity so the planet is 3 times as fast at perihelion as at aphelion (e = 0.5).

Common mistake

Planets move at constant speed; equal areas proves the inverse-square law.

In NEET

10 years of papers

Asked 2 times in 10 years of NEET.

See the past questions: Gravitation, Gravitation (chapter)

In JEE Main

42 shifts analysed

39 questions from Gravitation across the 42 JEE Main shifts Lumi has analysed (2017–2026).

See the past questions

The idea behind it

NCERT §7.2

  • Law of areas: in any two equal stretches of time, the sun–planet line covers the same area. A planet therefore speeds up near the sun and slows down far from it.
  • In a short time Δt the sun–planet line sweeps ΔA = ½ |r × v Δt|, so ΔA/Δt = L/(2m), where L = r × p is the planet's angular momentum.
  • Gravity on a planet points along the sun–planet line (a central force), so it exerts no torque about the sun; L stays constant and so does ΔA/Δt.
  • The law of areas therefore holds for any central force, not only for an inverse-square one.
  • At perihelion and aphelion r and v are perpendicular, so m r_P v_P = m r_A v_A, giving v_P / v_A = r_A / r_P: the planet is fastest at perihelion.
  • The half of the orbit around the aphelion encloses the larger area, so the planet spends the longer time on that half.

Questions

5 answers

What does the "Equal areas in equal times" simulation show?
A planet on an ellipse sweeps shaded sectors in equal time intervals; speed and KE at each point; v_P/v_A = r_A/r_P.
What mistake does the "Equal areas in equal times" simulation fix?
A common mistake it clears up: planets move at constant speed; equal areas proves the inverse-square law.
Has NEET asked about this idea?
Yes. NEET has asked about this idea 2 times in 10 years of papers.
Does JEE Main ask questions from Gravitation?
Yes. JEE Main asked 39 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
Is this simulation free?
Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "The law of areas" in Gravitation (Class 11 Physics).

Embed this simulation

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