Kepler's three laws of planetary motion

Grade 9 Science Worksheet - Challenge Me

Circle the best answer.

1. Read this first

   Rule card

   Perihelion = a × (1 − e); aphelion = a × (1 + e); a = 2.5 AU, e = 0.6.

2. 1.

   A new object has a = 2.5 AU and e = 0.6. What are its perihelion and aphelion distances (a × (1 − e) and a × (1 + e)), by Esme's math?

   • 1.0 AU and 4.0 AU
   • 1.9 AU and 3.1 AU
   • 2.5 AU at both points
   • 1.0 AU and 4.0 AU, fastest at 4.0 AU
3. 2.

   T² = a³; a = 2.5 AU. The same object has a = 2.5 AU. About how long is its orbit, by Jun's math?

   • About 2.5 years
   • About 4.0 years
   • About 1.6 years
   • About 15.6 years
4. 3.

   Earth's orbit with perihelion in early January (NOAA) and the tilted axis drawn. Luz's friend says Earth is closer to the Sun in summer, which is why summer is hot. Which response is best?

   • Disagree: Earth's distance does not change
   • Disagree: Earth is closest in January; tilt causes the seasons
   • Agree: closer means hotter, so summer
   • Agree: Earth is closest in July
5. 4.

   Milo's cousin says planets move at a steady speed around circles with the Sun at the center. Which response is best?

   • Disagree: they move fastest when farthest
   • Disagree: ellipses with the Sun at a focus, faster when closer
   • Agree: orbits are perfect circles
   • Agree, and that is why we have seasons

6. Orbits (NASA)

   Planet	a (AU)	T (years)	Speed (km/s)
   Earth	1.000	1.000	29.8
   Jupiter	5.20	11.86	13.1

7. 5.

   Noah's friend says outer planets take longer only because their paths are longer. Jupiter's path is 5.2 times Earth's, but its year is 11.86 times. Which response is best?

   • Agree: the period grows as a, not a^1.5
   • Agree: they move at Earth's speed
   • Disagree: outer planets move faster
   • Disagree: their paths are longer and they also move slower
8. 6.

   T² = a³; Saturn a ≈ 9.57 AU; NASA period 10,747 days (about 29.4 years). Saturn orbits at a = 1,432 ÷ 149.6 ≈ 9.57 AU. Predict its period, by Ren's math.

   • About 877 years
   • About 9.6 years
   • About 29.6 years, close to NASA's 29.4
   • About 3.1 years
9. 7.

   T² = a³; T = 0.615 years. A planet's year is 0.615 Earth years. Predict its distance from the Sun, by Tala's math.

   • About 0.72 AU
   • About 0.48 AU
   • About 1.6 AU, farther than Earth
   • About 0.62 AU

10. Orbits (NASA Planetary Fact Sheet)

    Planet	a (AU)	T (years)	e
    Mercury	0.387	0.241	0.206
    Earth	1.000	1.000	0.017
    Mars	1.524	1.881	0.094
    Jupiter	5.20	11.86	0.049

11. 8.

    Average speed is proportional to a ÷ T. Using Earth's 29.8 km/s, about how fast does Mars move (a = 1.524 AU, T = 1.881 years), by Zee's math?

    • About 29.8 km/s, Earth's speed
    • About 36.8 km/s
    • About 45 km/s
    • About 24 km/s
12. 9.

    Why do Mercury's speed and distance change much more around its orbit than Earth's, by Ari's reading?

    • Its orbit is a circle
    • Its orbit is less eccentric than Earth's
    • Mercury spins faster on its axis
    • Its orbit is far more eccentric
13. 10.

    T² is proportional to a³ around the same planet; B's a = 4 × A's. Two moons orbit the same planet. Moon B's average distance is 4 times moon A's. How do their periods compare, by Bo's math?

    • B takes 8 times as long
    • B takes 64 times as long
    • B takes 1/8 as long
    • B takes 4 times as long