Kepler's three laws of planetary motion

Grade 9 Science Worksheet

Circle the best answer.

1. Read this first

   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

2. 1.

   Check Kepler's third law for Mars: compare 1.524³ with 1.881², by Bo's math.

   • Both are about 3.54, so the law holds
   • It works for Earth alone
   • 3.54 and 1.88 differ, so it fails
   • 1.524 and 1.881 differ, so it fails
3. 2.

   T² = a³ (T in years, a in AU); a = 4. A dwarf planet orbits the Sun at a = 4 AU. What is its period, by Esme's math?

   • 64 years
   • 2 years
   • 4 years
   • 8 years
4. 3.

   T² = a³ (T in years, a in AU); T = 27. An asteroid takes 27 years to orbit the Sun. What is its average distance, by Jun's math?

   • 27 AU
   • 9 AU
   • 3 AU
   • 140 AU

5. Mars (NASA)

   Point	Speed (km/s)	Distance (million km)
   perihelion	26.50	206.65
   aphelion	21.97	249.26

6. 4.

   NASA: Mars moves at 26.50 km/s at perihelion (206.65 million km) and 21.97 km/s at aphelion (249.26 million km). Compare speed × distance at each point, by Kira's math.

   • Mars is faster at aphelion
   • Speed × distance doubles from one point to the other
   • The speed is the same at both points
   • Both are about 5,476: faster goes with closer

7. Earth (NASA)

   Point	Speed (km/s)	Distance (million km)
   perihelion	30.29	147.1
   aphelion	?	152.1

8. 5.

   Earth moves at 30.29 km/s at perihelion (147.1 million km). With speed × distance staying the same, how fast is it at aphelion (152.1 million km), by Luz's math?

   • About 4,455 km/s
   • About 30.29 km/s, unchanged
   • About 29.3 km/s
   • About 31.3 km/s

9. Mars (NASA)

   Point	Distance (million km)
   perihelion	206.7
   aphelion	249.3

10. 6.

    Mars's aphelion is 249.3 and perihelion 206.7 million km (NASA). What is its eccentricity, by Pia's math?

    • About 1.21
    • About 0.83
    • About 42.6
    • About 0.093

11. Earth (NASA)

    Point	Distance (million km)
    perihelion	147.1
    aphelion	152.1
    average	149.6

12. 7.

    Earth's distance ranges from 147.1 to 152.1 million km, averaging 149.6. About what percent of the average is that change, by Ren's math?

    • About 0%, since the orbit is a circle
    • About 30%, enough to cause the seasons
    • About 300%
    • About 3% of the average distance

13. Mercury's orbital speed (NASA)

    Speed	Value
    maximum	58.97 km/s
    minimum	38.86 km/s

14. 8.

    NASA gives Mercury's fastest speed as 58.97 km/s and its slowest as 38.86 km/s. How many times faster is it at perihelion, by Tala's math?

    • About 20 times
    • About 1.5 times
    • About 0.66 times
    • Exactly 1 time
15. 9.

    In which month is Earth moving fastest along its orbit, by Zee's reading?

    • June, in northern summer
    • July, near aphelion
    • Each month at the same speed
    • January, near perihelion
16. 10.

    A comet's orbit has e = 0.97; Earth's has e = 0.017. How do their speed changes compare, by Ari's reading?

    • Earth's speed changes more
    • The comet's speed changes far more
    • Neither changes, since orbits are circles
    • Both keep a constant speed