Worksheet: Elliptical Motion

In this worksheet, we will practice calculating the properties of the orbits of objects that move along elliptical orbits.

Q1:

Callisto is a moon that orbits Jupiter. The orbit of Callisto around Jupiter is elliptical, with an eccentricity of 0.00740. The semimajor axis of Callisto’s orbit is 1 . 8 8 × 1 0 km.

How far away from Jupiter is Callisto when it is at its closest to Jupiter? Give your answer to 3 significant figures.

  • A 1 . 8 9 × 1 0 km
  • B 1 . 8 7 × 1 0 km
  • C 1 . 9 1 × 1 0 km
  • D 1 . 8 2 × 1 0 km
  • E 1 . 8 5 × 1 0 km

How far away from Jupiter is Callisto when it is at its farthest from Jupiter? Give your answer to 3 significant figures.

  • A 1 . 8 2 × 1 0 km
  • B 1 . 9 1 × 1 0 km
  • C 1 . 8 5 × 1 0 km
  • D 1 . 8 7 × 1 0 km
  • E 1 . 8 9 × 1 0 km

Q2:

Saturn moves along an elliptical orbit around the Sun. The semimajor axis of its orbit is 9.58 AU, and the eccentricity of its orbit is 0.0565.

What is the distance between Saturn and the Sun when Saturn is at the perihelion of its orbit? Give your answer to 3 significant figures.

What is the distance between Saturn and the Sun when Saturn is at the aphelion of its orbit? Give your answer to 3 significant figures.

Q3:

Jupiter moves along an elliptical orbit around the Sun. When Jupiter is at the perihelion of its orbit, it is 4.95 AU away from the Sun. When Jupiter is at the aphelion of its orbit, it is 5.46 AU away from the Sun. What is the eccentricity of Jupiter’s orbit? Give your answer to 3 significant figures.

Q4:

The Moon moves along an elliptical orbit around Earth. When the Moon is at the perigee of its orbit, it is 363,000 km away from Earth. When the Moon is at the apogee of its orbit, it is 405,000 km away from Earth. What is the eccentricity of the Moon’s orbit? Give your answer to 3 significant figures.

Q5:

The diagram shows an ellipse. Which two points mark the foci of the ellipse?

  • A 𝐴 and 𝐼
  • B 𝐶 and 𝐺
  • C 𝐸 , 𝐷 , and 𝐹
  • D 𝐷 and 𝐹
  • E 𝐵 and 𝐻

Q6:

The diagram shows an ellipse. The distance between the two foci of the ellipse is 12 AU, and the major axis has a length of 15 AU. What is the eccentricity of the ellipse?

Q7:

The diagram shows an ellipse that has an eccentricity of 0.82. If the semimajor axis has a length of 5.0 AU, what is the distance between the focus and the center of the ellipse?

Q8:

The diagram shows an ellipse. The distance between the two foci of the ellipse is 0.68 AU, and the ellipse has an eccentricity of 0.41. What is the length of the major axis of the ellipse? Give your answer to 3 significant figures.

Q9:

Each of the following diagrams shows an ellipse. In which diagram does the blue line show the minor axis of the ellipse?

  • A
  • B
  • C
  • D
  • E

Q10:

Each of the following diagrams shows an ellipse. In which diagram does the blue line show the semiminor axis of the ellipse?

  • A
  • B
  • C
  • D
  • E

Q11:

Each of the following diagrams shows an ellipse. In which diagram does the blue line show the semimajor axis of the ellipse?

  • A
  • B
  • C
  • D
  • E

Q12:

The diagram shows a planet moving along an elliptical orbit around the Sun. Which of the points 𝐴 , 𝐵 , 𝐶 , 𝐷 , or 𝐸 marks the perihelion of the planet’s orbit?

  • A 𝐸
  • B 𝐶
  • C 𝐷
  • D 𝐵
  • E 𝐴

Q13:

The diagram shows an ellipse. If the distance between the focus and the center of the ellipse is 0.75 AU and the semimajor axis is 1.2 AU, what is the eccentricity of the ellipse?

Q14:

Each of the following diagrams shows an ellipse. In which diagram does the blue line show the major axis of the ellipse?

  • A
  • B
  • C
  • D
  • E

Q15:

The diagram shows a planet moving along an elliptical orbit around the Sun. Which of the points I, II, III, IV, or V marks the aphelion of the planet’s orbit?

  • AIII
  • BI
  • CV
  • DII
  • EIV

Q16:

The diagram shows the orbit of the Moon around Earth. What is the name given to point V on the diagram?

  • APerigee
  • BApastron
  • CApogee
  • DAphelion
  • EPerihelion

Q17:

The diagram shows the orbit of the Moon around Earth. What is the name given to point II on the diagram?

  • APerigee
  • BPerihelion
  • CApogee
  • DAphelion
  • EApastron

Q18:

The diagram shows a planet moving along an elliptical orbit around the Sun. The distance between the planet and the Sun when the planet is at its perihelion is 30 AU. The distance between the planet and the Sun when the planet is at its aphelion is 45 AU. What is the eccentricity of the planet’s orbit?

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