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Calculating the gravitational interaction of more than two objects is complicated and requires large computers. If one object (like the Sun in our solar system) dominates gravitationally, it is possible to calculate the effects of a second object in terms of small perturbations. This approach was used by John Couch Adams and Urbain Le Verrier to predict the position of Neptune from its perturbations of the orbit of Uranus and thus discover a new planet mathematically.
Christianson, G. “The Celestial Palace of Tycho Brahe.” Scientific American (February 1961): 118.
Gingerich, O. “Johannes Kepler and the Rudolphine Tables.” Sky&Telescope (December 1971): 328. Brief article on Kepler’s work.
Wilson, C. “How Did Kepler Discover His First Two Laws?” Scientific American (March 1972): 92.
Christianson, G. “Newton’s Principia : A Retrospective.” Sky&Telescope (July 1987): 18.
Cohen, I. “Newton’s Discovery of Gravity.” Scientific American (March 1981): 166.
Gingerich, O. “Newton, Halley, and the Comet.” Sky&Telescope (March 1986): 230.
Sullivant, R. “When the Apple Falls.” Astronomy (April 1998): 55. Brief overview.
Sheehan, W., et al. “The Case of the Pilfered Planet: Did the British Steal Neptune?” Scientific American (December 2004): 92.
Johannes Kepler: His Life, His Laws, and Time: http://kepler.nasa.gov/Mission/JohannesKepler/. From NASA’s Kepler mission.
Johannes Kepler: http://www.britannica.com/biography/Johannes-Kepler. Encyclopedia Britannica article.
Johannes Kepler: http://www-history.mcs.st-andrews.ac.uk/Biographies/Kepler.html. MacTutor article with additional links.
Noble Dane: Images of Tycho Brahe: http://www.mhs.ox.ac.uk/tycho/index.htm. A virtual museum exhibit from Oxford.
Sir Isaac Newton: http://www-groups.dcs.st-and.ac.uk/~history//Biographies/Newton.html. MacTutor article with additional links.
Sir Isaac Newton: http://www.luminarium.org/sevenlit/newton/newtonbio.htm. Newton Biography at the Luminarium.
Adams, Airy, and the Discovery of Neptune: http://www.mikeoates.org/lassell/adams-airy.htm. A defense of Airy’s role by historian Alan Chapman.
Mathematical Discovery of Planets: http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Neptune_and_Pluto.html. MacTutor article.
“Harmony of the Worlds.” This third episode of Carl Sagan’s TV series Cosmos focuses on Kepler and his life and work.
Tycho Brahe, Johannes Kepler, and Planetary Motion: https://www.youtube.com/watch?v=x3ALuycrCwI. German-produced video, in English (14:27).
Beyond the Big Bang: Sir Isaac Newton’s Law of Gravity: http://www.history.com/topics/enlightenment/videos/beyond-the-big-bang-sir-isaac-newtons-law-of-gravity. From the History Channel (4:35).
Sir Isaac Newton versus Bill Nye: Epic Rap Battles of History: https://www.youtube.com/watch?v=8yis7GzlXNM. (2:47).
Richard Feynman: On the Discovery of Neptune: https://www.youtube.com/watch?v=FgXQffVgZRs. A brief black-and-white Caltech lecture (4:33).
Is it possible to escape the force of gravity by going into orbit around Earth? How does the force of gravity in the International Space Station (orbiting an average of 400 km above Earth’s surface) compare with that on the ground?
What is the momentum of an object whose velocity is zero? How does Newton’s first law of motion include the case of an object at rest?
Evil space aliens drop you and your fellow astronomy student 1 km apart out in space, very far from any star or planet. Discuss the effects of gravity on each of you.
A body moves in a perfectly circular path at constant speed. Are there forces acting in such a system? How do you know?
As friction with our atmosphere causes a satellite to spiral inward, closer to Earth, its orbital speed increases. Why?
Use a history book, an encyclopedia, or the internet to find out what else was happening in England during Newton’s lifetime and discuss what trends of the time might have contributed to his accomplishments and the rapid acceptance of his work.
Two asteroids begin to gravitationally attract one another. If one asteroid has twice the mass of the other, which one experiences the greater force? Which one experiences the greater acceleration?
How does the mass of an astronaut change when she travels from Earth to the Moon? How does her weight change?
If there is gravity where the International Space Station (ISS) is located above Earth, why doesn’t the space station get pulled back down to Earth?
Compare the density, weight, mass, and volume of a pound of gold to a pound of iron on the surface of Earth.
If identical spacecraft were orbiting Mars and Earth at identical radii (distances), which spacecraft would be moving faster? Why?
By what factor would a person’s weight be increased if Earth had 10 times its present mass, but the same volume?
Suppose astronomers find an earthlike planet that is twice the size of Earth (that is, its radius is twice that of Earth’s). What must be the mass of this planet such that the gravitational force ( F _{gravity} ) at the surface would be identical to Earth’s?
What is the semimajor axis of a circle of diameter 24 cm? What is its eccentricity?
If 24 g of material fills a cube 2 cm on a side, what is the density of the material?
If 128 g of material is in the shape of a brick 2 cm wide, 4 cm high, and 8 cm long, what is the density of the material?
If the major axis of an ellipse is 16 cm, what is the semimajor axis? If the eccentricity is 0.8, would this ellipse be best described as mostly circular or very elongated?
What is the average distance from the Sun (in astronomical units) of an asteroid with an orbital period of 8 years?
What is the average distance from the Sun (in astronomical units) of a planet with an orbital period of 45.66 years?
In 1996, astronomers discovered an icy object beyond Pluto that was given the designation 1996 TL 66. It has a semimajor axis of 84 AU. What is its orbital period according to Kepler’s third law?
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