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
   • 1.9 AU and 3.1 AU
   • 1.0 AU and 4.0 AU
   • 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 4.0 years
   • About 15.6 years
   • About 2.5 years
   • About 1.6 years
4. 3.

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

   • About 4 times faster at perihelion
   • About 4 times faster at aphelion
   • The same speed at both
   • 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: Earth is closest in July
   • Agree: closer means hotter, so summer
   • Disagree: Earth's distance does not change
   • Disagree: Earth is closest in January; tilt causes the 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: they move at Earth's speed
   • Disagree: their paths are longer and they also move slower
   • Agree: the period grows as a, not a^1.5
   • Disagree: outer planets move faster

8. 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

9. 6.

   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
   • 5.20 and 11.86 differ, so it fails
   • It fits for inner planets alone
   • 140.6 against 11.86, so it fails
10. 7.

    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
11. 8.

    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

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