The Two-Body Problem, Orbital Energy and Kepler's First Two Laws · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Equal areas, bound orbits, wobbling suns

Science · Forces & Motion · ages 20-21
Name ______________________   Date ____________

  1. Total orbital energy is negative. What does that mean?

    • The object barely escapes
    • The object leaves for good
    • The orbit is bound and looping

  2. Why does a planet sweep equal areas in equal times?

    • Gravity is central, so angular momentum is conserved
    • The Sun pushes the planet along its path
    • All orbits are perfect circles

  3. A planet moves fastest at aphelion, its farthest point from the Sun.

    Circle one:   True   False

  4. You know position and velocity at one point. How do you find the speed at a new radius?

    • Assume the speed never changes
    • Divide the old speed by the new radius
    • Use energy conservation between the two radii

  5. Total energy is exactly zero. Which path does the object follow?

    • A closed ellipse
    • A parabola that just barely escapes
    • A plunge straight into the star

  6. Why does the Sun also move?

    • The solar wind pushes the Sun around
    • Both bodies orbit their shared centre of mass
    • Sunlight pressure rocks it back and forth

  7. An object has kinetic energy 4 units and potential energy minus 10 units. What is its total orbital energy?

    Answer: ______________

  8. A starlight spectrum shifts red and blue in a steady rhythm. What is the likely cause?

    • The star cooling down and shrinking
    • Dust dimming the telescope at random
    • An unseen planet tugging its star around
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Equal areas, bound orbits, wobbling suns W1-mt_CjHFftkB6M-s1

  1. The orbit is bound and looping · Negative total energy means gravity wins and the path closes.
  2. Gravity is central, so angular momentum is conserved · A purely radial pull cannot twist the motion, fixing the areal rate.
  3. False · Equal areas force the highest speed at perihelion, the nearest point.
  4. Use energy conservation between the two radii · Kinetic plus potential at the new radius must equal the known total.
  5. A parabola that just barely escapes · Zero is the boundary case between bound loops and escape.
  6. Both bodies orbit their shared centre of mass · Each body pulls the other, so both circle the balance point.
  7. -6 · 4 plus minus 10 is minus 6, so the object is bound.
  8. An unseen planet tugging its star around · The periodic shift is the star wobble from an orbiting companion.
Worksheet · LightMySky