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Class 11  »  Physics  »  Gravitation

Kepler's Laws of Planetary Motion - UNSOLVED PRACTICE SET

Class 11

Chapter: Gravitation | Topic: Keplers Laws of Planetary Motion

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Class 11

KEPLER'S LAWS OF PLANETARY MOTION - UNSOLVED PRACTICE SET

Topic: Keplers Laws of Planetary Motion

Time: 40 mins | Marks: 30 | Difficulty: Medium

Multiple Choice Questions

Q1. According to Kepler's first law, the orbit of a planet around the Sun is:

  1. A perfect circle with the Sun at the centre
  2. An ellipse with the Sun at one of the foci
  3. A parabola with the Sun at the vertex
  4. A straight line passing through the Sun

Q2. Kepler's second law is a consequence of:

  1. Conservation of energy
  2. Conservation of angular momentum
  3. Conservation of linear momentum
  4. Newton's third law

Q3. If the orbital period of a planet is 8 times that of Earth, its mean distance from the Sun is:

  1. 2 AU
  2. 4 AU
  3. 8 AU
  4. 16 AU

Q4. A planet moves fastest in its orbit when it is:

  1. Farthest from the Sun
  2. Closest to the Sun
  3. At the midpoint of its orbit
  4. Moving perpendicular to the radius vector

Q5. Kepler's laws of planetary motion apply to:

  1. Only planets orbiting the Sun
  2. Any system where a smaller body orbits a larger mass under gravity
  3. Only circular orbits
  4. Only elliptical orbits in our solar system

Q6. The areal velocity of a planet i

  1. Constant throughout the orbit
  2. Maximum at aphelion
  3. Maximum at perihelion
  4. Zero at the foci

Short Answer Questions

Q7. State Kepler's three laws of planetary motion in your own words.

Q8. A comet has a very elliptical orbit. At what point in its orbit is its speed maximum, and at what point is it minimum? Explain using Kepler's second law.

Q9. The mean distance of Mars from the Sun is 1.52 AU. Calculate its orbital period in Earth years using Kepler's third law.

Q10. In your school astronomy club, students observe that Mercury orbits the Sun in 88 days while Earth takes 365 days. Without using a calculator, explain how you would estimate Mercury's orbital radius compared to Earth's.

Q11. Why are Kepler's laws called "empirical laws"? How did Newton provide a theoretical foundation for them?

Q12. A satellite orbits Earth in an elliptical path. At one point, it is 400 km above Earth's surface, and at another, it is 600 km above. At which point is its speed greater? Explain.

Long Answer Questions

Q13. State and explain Kepler's three laws of planetary motion with diagrams. Show how Kepler's second law is a consequence of conservation of angular momentum. Discuss the significance of these laws in understanding the solar system.

Q14. The orbital period of Jupiter is 11.86 years and its mean orbital radius is 5.2 AU. The orbital period of Saturn is 29.5 years.

(a) Verify Kepler's third law using Jupiter's data.

(b) Calculate Saturn's mean orbital radius using Kepler's third law.

(c) Compare the orbital speeds of Jupiter and Saturn.

(d) Discuss why outer planets have longer orbital periods.

Q15. A hypothetical planet X orbits a star in an elliptical orbit with semi-major axis 4 AU and eccentricity 0.5.

(a) Calculate the perihelion and aphelion distances.

(b) If the planet's speed at perihelion is 40 km/s, calculate its speed at aphelion.

(c) Explain why the planet spends more time near aphelion than near perihelion.

(d) Sketch the orbit showing the star at one focus, and mark perihelion and aphelion.

Application-Based Problems

Q16. The planet Neptune was discovered through mathematical predictions based on Kepler's laws. Given that Neptune's orbital period is 164.8 years:

(a) Calculate its mean distance from the Sun in AU using Kepler's third law.

(b) If Uranus orbits at 19.2 AU with a period of 84 years, verify that Kepler's third law holds for both planets.

(c) Calculate the ratio of Neptune's orbital speed to Uranus's orbital speed.

(d) Explain how deviations from Kepler's laws led to the discovery of Neptune.

Q17. An asteroid orbits the Sun with a period of 8 years. Its closest approach to the Sun (perihelion) is 2 AU.

(a) Calculate the semi-major axis of the asteroid's orbit.

(b) Calculate the aphelion distance.

(c) If the asteroid's speed at perihelion is 30 km/s, calculate its speed at aphelion.

(d) Calculate the areal velocity of the asteroid (in AU²/year).

(e) Verify that the asteroid's orbit is consistent with Kepler's laws.

Q18. In a school project, students create a scale model of the solar system using Kepler's third law. They represent Earth's orbit as a circle of radius 10 cm.

(a) What should be the radius of Mercury's orbit (period = 0.24 years)?

(b) What should be the radius of Venus's orbit (period = 0.62 years)?

(c) What should be the radius of Mars's orbit (period = 1.88 years)?

(d) Calculate the orbital speed of each planet in the model if Earth completes one orbit in 10 seconds.

(e) Discuss the limitations of this model in representing the actual solar system.


Total: 30 Marks | Time: 40 mins

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