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

   At 1.0 AU (perihelion) and 4.0 AU (aphelion), how do the object's speeds compare, by Kira's math?

   • The same speed at both
   • About 4 times faster at perihelion
   • About 4 times faster at aphelion
   • About 16 times faster at perihelion
5. 4.

   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?

   • Agree: closer means hotter, so summer
   • Disagree: Earth is closest in January; tilt causes the seasons
   • Agree: Earth is closest in July
   • Disagree: Earth's distance does not change
6. 5.

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

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

7. Orbits (NASA)

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

8. 6.

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

9. 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

10. 7.

    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?

    • It fits for inner planets alone
    • 140.6 against 11.86, so it fails
    • 5.20 and 11.86 differ, so it fails
    • Both are about 141, so it fits
11. 8.

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

12. 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

13. 9.

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