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
   • 1.524 and 1.881 differ, so it fails
   • 3.54 and 1.88 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
   • 8 years
   • 2 years
   • 4 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?

   • 140 AU
   • 3 AU
   • 9 AU
   • 27 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
   • Both are about 5,476: faster goes with closer
   • Speed × distance doubles from one point to the other
   • The speed is the same at both points

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 29.3 km/s
   • About 30.29 km/s, unchanged
   • About 31.3 km/s
9. 6.

   In the equal-area drawing, the slice near perihelion is short and wide; the slice near aphelion is long and thin. Each took 30 days. Which arc along the orbit is longer, by Milo's reading?

   • Neither; equal times mean equal distances
   • The arc near aphelion
   • The arcs are equal, since the times are equal
   • The arc near perihelion, so it moved faster there

10. Mercury (NASA)

    Point	Distance (million km)
    perihelion	46.0
    aphelion	69.8

11. 7.

    Mercury's aphelion is 69.8 and perihelion 46.0 million km. Using e = (aphelion − perihelion) ÷ (aphelion + perihelion), what is e, by Noah's math?

    • 0, since it is a circle
    • About 23.8
    • About 0.21
    • About 0.66

12. Earth (NASA)

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

13. 8.

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

14. Mercury's orbital speed (NASA)

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

15. 9.

    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 1.5 times
    • Exactly 1 time
    • About 0.66 times
    • About 20 times
16. 10.

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

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