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?

   • 2.5 AU at both points
   • 1.0 AU and 4.0 AU
   • 1.0 AU and 4.0 AU, fastest at 4.0 AU
   • 1.9 AU and 3.1 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 15.6 years
   • About 1.6 years
   • About 4.0 years
4. 3.

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

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

5. Orbits (NASA)

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

6. 4.

   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
   • Disagree: their paths are longer and they also move slower
   • Disagree: outer planets move faster
   • Agree: they move at Earth's speed

7. 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

8. 5.

   Check Kepler's third law for Jupiter: a = 5.20 AU, T = 11.86 years. What do a³ and T² give, by Pia's math?

   • Both are about 141, so it fits
   • 140.6 against 11.86, so it fails
   • 5.20 and 11.86 differ, so it fails
   • It fits for inner planets alone
9. 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 9.6 years
   • About 3.1 years
   • About 877 years
   • About 29.6 years, close to NASA's 29.4
10. 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 0.62 AU
    • About 0.48 AU
    • About 0.72 AU
    • About 1.6 AU, farther than Earth

11. 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

12. 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 45 km/s
    • About 36.8 km/s
    • About 24 km/s
    • About 29.8 km/s, Earth's speed
13. 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
14. 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 64 times as long
    • B takes 4 times as long
    • B takes 8 times as long
    • B takes 1/8 as long