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    • Physics Cup – TalTech 2024
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      • Problem 1 - Magnetized ball
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      • Problem 5 - Satellite
    • Physics Cup – TalTech 2021
      • Problem 1 - Dumbbell in a magnetic field
      • Problem 2 - Comet's orbit
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      • Problem 5 - Nonlinear circular resonator
    • Physics Cup – TalTech 2020
      • Problem 0 - Sheet resistance
      • Problem 1 - Small oscillations of a system in an electric field
      • Problem 2 - Staircase-like surface of a crystal
      • Problem 3 - Thread breaking point
      • Problem 4 - Heat flux between plates
      • Problem 5 - Lens position reconstruction
    • Physics Cup – TalTech 2019
      • Problem 1 - Added mass
      • Problem 2 - Heat engines
      • Problem 3 - Bouncing ball
      • Problem 4 - Grid of resistors
      • Problem 5 - Diffraction pattern
    • Physics Cup – 2018
      • Problem 1 - Lattice of resistors
      • Problem 2 - Spaceship missiles
      • Problem 3 - Loop inductance
      • Problem 4 - V-shaped vessel
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    • Physics Cup – 2017
      • Problem 1 - Interaction force
      • Problem 2 - N-gon resistance
      • Problem 3 - Electron gas temperature
      • Problem 4 - Lens position
    • Physics Cup – WoPhO 2013
      • Problem 1 - Dodecahedron capacitance
      • Problem 2 - Ring on rails
      • Problem 3 - Gas bubble in water
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      • Problem 5 - Magnetic levitation
    • Physics Cup – IPhO 2012
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    • PC2021: Intermediate results, Problem 5, week 6
    • PC2021: Intermediate results, Problem 4, week 8
    • PC2021: Intermediate results, Problem 4, week 7
    • PC2021: Intermediate results, Problem 5, week 3
    • PC2021: Intermediate results, Problem 5, week 2
    • PC2021: Intermediate results, Problem 4, week 6
    • PC2021: Intermediate results, Problem 5, week 1
    • PC2021: Intermediate results, Problem 4, week 5
    • 2021-P3 Best Solutions and Final Results
    • PC2021: Intermediate results, Problem 4, week 3
    • PC2021: Intermediate results, Problem 4, week 2
    • PC2021: Intermediate results, Problem 3, week 6
    • PC2021: Intermediate results, Problem 4, week 1
    • PC2021: Intermediate results, Problem 3, week 5
    • PC2021: Intermediate results, Problem 3, week 4
    • PC2021: Intermediate results, Problem 3, week 3
    • 2021-P2 Best Solutions and Final Results
    • PC2021: Intermediate results, Problem 3, week 1
    • PC2021: Intermediate results, Problem 2, week 5
    • PC2021: Intermediate results, Problem 2, week 4
    • PC2021: Intermediate results, Problem 2, week 3
    • 2021-P1 Best Solutions and Final Results
    • PC2021: Intermediate results, Problem 2, week 2
    • PC2021: Intermediate results, Problem 1, week 7
    • PC2021: Intermediate results, Problem 2, week 1
    • PC2021: Intermediate results, Problem 1, week 6
    • PC2021: Intermediate results, week 5
    • PC2021: Intermediate results, week 4
    • PC2021: Intermediate results, week 3
    • PC2021: Intermediate results, week 2
    • PC2021: Intermediate results, week 1
    • Problem 2; intermediate results, weeks 6
    • Problem 3; intermediate results, week 6
    • Problem 4; intermediate results, weeks 5,6
      • Problem 4, weeks 4-6
    • Problem 5; intermediate results, week 6

Problem 5 – Hint 3

Use of the Runge-Lenz vector to construct the hodograph of the satellite as a circle. To find the distance of the centre of this circle from the origin, it is helpful to consider the power of the origin with respect to the circle.

Please submit the solution to this problem via e-mail to physcs.cup@gmail.com.

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