Kepler's three laws of planetary motion

Grade 9 Science Worksheet - Building Confidence

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.

   Which planet in the table has the most stretched orbit, by Kira's reading?

   • Mercury, e = 0.206
   • Mars, e = 0.094
   • Earth, e = 0.017
   • Jupiter, e = 0.049
3. 2.

   two shaded slices of equal area. What does Kepler's second law say a line from the Sun to a planet does, by Jun's reading (NASA)?

   • Sweeps equal areas in equal times
   • Sweeps equal distances in equal times
   • Sweeps larger areas when far away
   • Sweeps equal angles in equal times
4. 3.

   Orbit diagram with perihelion and aphelion marked. Where in its orbit does a planet move fastest, by Luz's reading?

   • Closest to the Sun, at perihelion
   • Halfway between the two
   • Farthest from the Sun, at aphelion
   • At the same speed everywhere

5. Earth's orbital speed (NASA)

   Speed	Value
   maximum	30.29 km/s
   minimum	29.29 km/s

6. 4.

   NASA gives Earth's orbital speed as 30.29 km/s at most and 29.29 km/s at least. Where is Earth when it moves at 30.29 km/s, by Milo's reading?

   • At both points equally
   • At aphelion, farthest from the Sun
   • At perihelion, closest to the Sun
   • In early July, its farthest point

7. 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

8. 5.

   Which planet in the table takes longest to orbit the Sun, by Noah's reading?

   • Mercury, the closest
   • Jupiter, the farthest out
   • They each take one year
   • Mercury, since it moves fastest
9. 6.

   Mars orbits at 1.524 AU. What is its orbital period in the table, by Pia's reading?

   • 1.524 years, the same as its distance
   • 0.53 years, shorter than Earth's
   • 3.54 years, its distance cubed
   • 1.881 years
10. 7.

    Four equation cards, labeled A to D. Which equation is Kepler's third law, with T in years and a in AU, by Ren's reading?

    • T³ = a²
    • T × a = 1
    • T² = a³
    • T = a

11. Mercury (NASA)

    Point	Distance (million km)
    perihelion	46.0
    aphelion	69.8

12. 8.

    NASA lists Mercury's perihelion as 46.0 and its aphelion as 69.8 million km. By how much does its distance from the Sun change, by Tala's math?

    • 0 km, since its orbit is a circle
    • 23.8 million km
    • 115.8 million km
    • 57.9 million km

13. Earth (NASA)

    Point	Distance (million km)
    perihelion	147.1
    aphelion	152.1

14. 9.

    Earth is closest to the Sun in early January (NOAA). Why is January not summer in the Northern Hemisphere, by Zee's reading?

    • Earth's orbit is a perfect circle
    • Seasons come from Earth's tilt, not its distance
    • The 5 million km change sets the seasons
    • January is summer everywhere on Earth
15. 10.

    Earth's orbital eccentricity is 0.017 (NASA). What does that tell Esme about the shape of the orbit?

    • It is a perfect circle
    • It is stretched enough to cause the seasons
    • It is very stretched, like a comet's
    • It is very nearly a circle