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 15.6 years
   • About 4.0 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 16 times faster at perihelion
   • About 4 times faster at perihelion
   • The same speed at both
   • About 4 times faster at aphelion
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?

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

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

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?

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

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?

    • 5.20 and 11.86 differ, so it fails
    • 140.6 against 11.86, so it fails
    • Both are about 141, so it fits
    • It fits for inner planets alone
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 24 km/s
    • About 36.8 km/s
    • About 29.8 km/s, Earth's speed
    • About 45 km/s
12. 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 far more eccentric
    • Its orbit is a circle
    • Its orbit is less eccentric than Earth's
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 64 times as long
    • B takes 1/8 as long
    • B takes 4 times as long
    • B takes 8 times as long