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, fastest at 4.0 AU
   • 1.9 AU and 3.1 AU
   • 1.0 AU and 4.0 AU
   • 2.5 AU at both points
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 15.6 years
   • About 4.0 years
   • About 1.6 years
   • About 2.5 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 16 times faster at perihelion
   • About 4 times faster at aphelion
   • The same speed at both
   • About 4 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
   • Agree: Earth is closest in July
   • Disagree: Earth is closest in January; tilt causes the seasons
   • 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: orbits are perfect circles
   • Disagree: they move fastest when farthest
   • Agree, and that is why we have seasons
   • Disagree: ellipses with the Sun at a focus, faster when closer
7. 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 3.1 years
   • About 29.6 years, close to NASA's 29.4
8. 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 1.6 AU, farther than Earth
   • About 0.48 AU
   • About 0.62 AU

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. 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 24 km/s
    • About 45 km/s
    • About 36.8 km/s
11. 9.

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

    • Mercury spins faster on its axis
    • Its orbit is a circle
    • Its orbit is far more eccentric
    • Its orbit is less eccentric than Earth's
12. 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 1/8 as long
    • B takes 64 times as long
    • B takes 8 times as long
    • B takes 4 times as long