AstroTutor - Guided Tour and Worksheet for Kepler's Laws

Guided Tour

Worksheet

Print out this page and follow along while viewing the animation. Then answer the questions based on information from the description and the animation.

Animation Guided Tour

1. Kepler's 1st Law:
   
   
   1. Earth, as well as planets, asteroids, and some comets, orbits the Sun in an elliptical path.
      
      
   2. Sun is located at one of the two foci of the ellipse.
      
      
   3. Earth travels faster when it is closest to Sun (perihelion), slower when it is most distant (aphelion).
   
   
2. This fact leads to Kepler's 2nd Law:
   
   
   1. Mathematically expressed, the area swept out by a line from Sun to Earth is the same for two or more intervals of time that are the same.
      
      
   2. In the animation, Earth sweeps out 70 squares while traveling from point a to point b in one month while it is close to aphelion. Likewise, Earth sweeps out 70 squares while traveling from point c to point d in one month while it is close to perihelion, even though the actual distance traveled between a and b is less than that between c and d.
   
   
3. Kepler's 3rd Law:
   
   
   1. Although it is not demonstrated in the animation, the more distant a planet (or other orbiting object) is from Sun, the longer it requires to orbit Sun once.
      
      
   2. Mathematically expressed, the relationship between an object's average distance from Sun (A) and the period of time required to orbit Sun (P) once is expressed by the equation P2 = A3
      
      
   3. For use with objects in the solar system, if A is expressed in units of the astronomical units (AU), P is expressed in Earth years.

Animation Worksheet

1. Why did the Ptolemaic System, which placed Earth at the center of the universe, last for so long? What was the new technology that was responsible for its demise? For what purpose was that new technology devised?
   
   
   
   
   
   
   
   
2. What was the inherent flaw in the Copernican System, which replaced the Ptolemaic System, that made it equally inaccurate in predicting the future positions of planets?
   
   
   
   
   
   
   
   
3. The person who was responsible for the revision of the Copernican System that made it more accurate than the Earth-centered System of Ptolemy was ____________________. For the precise observational data needed to revise the Copernican system, he was indebted to the skills of _______________________.
   
   
4. For what objects in the universe can the orbital principles devised by the scientist noted in Question (3) above be applied?
   
   
   
   
   
   
   
   
5. From what aspect of geometry are the shapes of the orbits of objects in space derived?
   
   
   
   
   
   
   
   
6. Sketch a proposed orbit that would allow your spacecraft to go from Earth to Moon, using the orbital principles discussed in the animation.
   
   
   
   
   
   
   
   
7. Approximately how many years are required for a planet whose distance from Sun is five (5) times greater than that of Earth to orbit Sun? What planet would you guess that is?
   
   
   
   
   
   
   
   
8. Pluto was discovered in 1930. What percentage of a complete orbit have astronomers been able to observe up to the present date? (Given: Pluto's average distance from Sun is 40 AU's)
   
   
   
   
   
   
   
   
9. At what time of the year is Earth at perihelion? Aphelion? What does Earth's varying distance from Sun have to do with climate on Earth?
   
   
   
   
   
   
   
   
10. Kepler's role in destroying support for the geocentric theory was his discovery that
    1. gravity is not a force, but the bending of space by matter.
    2. the idea of planets moving in perfect circles was false.
    3. the planet Venus goes through phases just like Moon.
    4. gold could be tarnished and changed into other metals.
    5. F = ma.
    
    
11. What happens on or about January 3rd of each year?
    1. The winter solstice.
    2. Sun crosses the ecliptic.
    3. Earth is most distant from Sun.
    4. The beginning of Lent, a religious observance that is astronomically based.
    5. Earth is closest to Sun.
    
    
12. In offering an alternative to the Earth-centered theory, Copernicus was motivated by
    1. the fact that the Ptolemaic system couldn't explain retrograde motion of the planets.
    2. the discovery that parallax proved Earth revolved around the Sun.
    3. telescopic observations that revealed that Sun and Moon were not perfect.
    4. his discovery of three laws of motion that explained the orbits of the planets.
    5. the simplicity and beauty of the heliocentric theory.
    
    
13. As a planet revolves around the Sun, its speed is greatest
    1. at aphelion.
    2. at the time of the summer solstice.
    3. at the time of the winter solstice.
    4. at perihelion.
    5. none of the above. The speed of a planet is constant.
    
    
14. Tycho Brahe is important in the history of astronomy because he
    1. discovered the laws that govern the behavior of planets orbiting Sun.
    2. discovered gravity.
    3. was a strong supporter of the Copernican hypothesis that all the planets orbit around Sun, not Earth.
    4. testified at the trial of Galileo, arguing that planets obey elliptical paths rather than circular paths.
    5. provided the precise observational data used by Kepler to discover the true shapes of planetary orbits.
    
    
15. Which of the following is not associated with Kepler's Laws of Planetary Motion?
    1. The force of attraction between Sun and Planet depends on their masses, and inversely on the distance between them squared.
    2. Planetary orbits are ellipses with the Sun at a focus.
    3. A line from Sun to planet sweeps out equal areas in equal intervals of time.
    4. The square of a planet's orbital period around Sun is proportional to its average distance from Sun cubed.
    5. They were discovered by Kepler prior to the condemnation and imprisonment of Galileo.
    
    
16. The elliptical shape of planetary orbits is only an approximation because
    1. the planets gravitationally influence one another.
    2. mathematics cannot be applied to objects in motion.
    3. the ellipse is not described by a mathematical equation.
    4. none of the above. Planetary orbits are exactly elliptical in shape.
    
    
17. Even Galileo, who was brave enough to confront the powerful Catholic Church with the radical notion of a Sun-centered universe instead of an Earth-centered universe, was not willing to accept the notion of planets going around Sun in elliptical orbits. This is because he ______.