Understanding Our Universe
3rd Edition
ISBN: 9780393614428
Author: PALEN, Stacy, Kay, Laura, Blumenthal, George (george Ray)
Publisher: W.w. Norton & Company,
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Chapter 3, Problem 11QAP
To determine
The correct statement of Kepler’s second law of planetary motion.
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Newton’s version of Kepler’s third law is: P2 = 4 π2 / [G (M1 + M2)] × a3. The space shuttle orbits 271 km above the Earth's surface. How often do the astronauts see a sunrise (in minutes)? Use the gravitational constant G = 6.67 × 10-11 m3 kg-1 s-2, the mass of the Earth M = 5.97 × 1024 kg, and the radius of the Earth to be 7000 km.
In the time of Johannes Kepler, it was believed that the orbit of Earth was circular, whereas the orbit of Mars was believed to be an oval (perhaps an ellipse), whose minor axis is 0.5% shorter than its major axis, so (a − b)/a ≈ 0.005. It was also known that the Sun is not at the center of this orbit; it is offset by about 10% of a. Kepler knew the geometry of ellipses very well, and recognized that this information made it quite likely that the orbit of Mars was actually an ellipse. Explain how he might have reached this conclusion (which was confirmed theoretically by Isaac Newton a half-century later).
Titan, the largest moon of Saturn has a mean orbital radius of 1.22x10^9 m. The orbital period of Titan is 15.95 days. Hyperion,
another moon of Saturn orbits at a mean radius of 1.48x10^9 m. Predict the orbital period of Hyperion in days.
Chapter 3 Solutions
Understanding Our Universe
Ch. 3.1 - Prob. 3.1CYUCh. 3.2 - Prob. 3.2CYUCh. 3.3 - Prob. 3.3CYUCh. 3.4 - Prob. 3.4CYUCh. 3.5 - Prob. 3.5CYUCh. 3 - Prob. 1QAPCh. 3 - Prob. 2QAPCh. 3 - Prob. 3QAPCh. 3 - Prob. 4QAPCh. 3 - Prob. 5QAP
Ch. 3 - Prob. 6QAPCh. 3 - Prob. 7QAPCh. 3 - Prob. 8QAPCh. 3 - Prob. 9QAPCh. 3 - Prob. 10QAPCh. 3 - Prob. 11QAPCh. 3 - Prob. 12QAPCh. 3 - Prob. 13QAPCh. 3 - Prob. 14QAPCh. 3 - Prob. 15QAPCh. 3 - Prob. 16QAPCh. 3 - Prob. 17QAPCh. 3 - Prob. 18QAPCh. 3 - Prob. 19QAPCh. 3 - Prob. 20QAPCh. 3 - Prob. 21QAPCh. 3 - Prob. 22QAPCh. 3 - Prob. 23QAPCh. 3 - Prob. 24QAPCh. 3 - Prob. 25QAPCh. 3 - Prob. 26QAPCh. 3 - Prob. 27QAPCh. 3 - Prob. 28QAPCh. 3 - Prob. 29QAPCh. 3 - Prob. 30QAPCh. 3 - Prob. 31QAPCh. 3 - Prob. 32QAPCh. 3 - Prob. 33QAPCh. 3 - Prob. 34QAPCh. 3 - Prob. 35QAPCh. 3 - Prob. 36QAPCh. 3 - Prob. 37QAPCh. 3 - Prob. 38QAPCh. 3 - Prob. 39QAPCh. 3 - Prob. 40QAPCh. 3 - Prob. 41QAPCh. 3 - Prob. 42QAPCh. 3 - Prob. 43QAPCh. 3 - Prob. 44QAPCh. 3 - Prob. 45QAP
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- Suppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter, (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2arrow_forwardLet gM represent the difference in the gravitational fields produced by the Moon at the points on the Earths surface nearest to and farthest from the Moon. Find the fraction gM/g, where g is the Earths gravitational field. (This difference is responsible for the occurrence of the lunar tides on the Earth.)arrow_forwardModel the Moons orbit around the Earth as an ellipse with the Earth at one focus. The Moons farthest distance (apogee) from the center of the Earth is rA = 4.05 108 m, and its closest distance (perigee) is rP = 3.63 108 m. a. Calculate the semimajor axis of the Moons orbit. b. How far is the Earth from the center of the Moons elliptical orbit? c. Use a scale such as 1 cm 108 m to sketch the EarthMoon system at apogee and at perigee and the Moons orbit. (The semiminor axis of the Moons orbit is roughly b = 3.84 108 m.)arrow_forward
- GRAVITY Problem-solving: Choose your answer from the dropdown provided on each item. The orbits of Earth and Venus around the Sun are nearly circular with a mean radius of Earth's orbit, re 1.50 x 10" m ,and a mean radius of Venus's orbit, rv = 1.08 x 10" m. The Earth's period of orbit around the Sun is 365.3 days and Venus is 224.7 days. Show whether Kepler's third law is obeyed. A.) For Earth's system B.) For Venus' system C.) Kepler's third law isarrow_forwardIn recent years, scientists have discovered hundreds of planets orbiting other stars. Some of these planets are in orbits that are similar to that of earth, which orbits the sun (MsunMsun = 1.99× 10^30kg) at a distance of 1.50 × 10^11 m, called 1 astronomical unit (1 auau). Others have extreme orbits that are much different from anything in our solar system. The following problem relates to one of these planets that follows circular orbit around its star. WASP-32b orbits with a period of only 2.7 days a star with a mass that is 1.1 times that of the sun. How many au from the star is this planet? Assume the orbital period of earth is 365 days.arrow_forwardIt is estimated that the Sun is 2.7 x 10 m away from the centre of the Milky Way Galaxy If the period of revolution for the galaxy is about 200 million years, what is the speed (in km/h) of the Sun going around the center of the galaxy? (9.68 x 10³ km/h)arrow_forward
- The table below illustrates data on Kepler's 3rd Law for the first six planets. Use it to estimate the orbital period of Asteroid Baade which has a semi-major axis of 2.55 AU | P (years) p2 a3 a (AU) Mercury 0.24 0.058 0.058 0.39 Venus 0.62 0.38 0.38 0.72 Earth 1.00 1.00 1.00 1.00 Mars 1.88 3.54 3.54 1.52 Jupiter 11.9 141 141 5.20 Saturn 29.5 868 868 9.54 A. 0.77 years B. 4.07 years C. 19.2 years D. 1.67 years Е. 50.2 yearsarrow_forwardThe position of a planet that a closest to and farthest from the sun are called its perihelion and aphelion respectively. We know that the Earth orbits around the Sun (as one focus) in an elliptical orbit with the perihelion distance of 1.47 x 10^8 km and the aphelion distance of 1.52 x 10^8 km. Find the Cartesian equation of the elliptical orbit.arrow_forwardAccording to Kepler's third law of planetary motion, the mean distance D, in millions of miles, from a planet in our solar system to the sun is related to the time P, in years, that it takes for the planet to complete a revolution around the sun, and the relationship is D = 93P 2/3. It takes the planet Pluto 248 years to complete a revolution around the sun. What is the mean distance from Pluto to the sun? What is the mean distance from Earth to the sun? Give your answers to the nearest million miles. from pluto to sun _____ million miles from earth to sun _____ million milesarrow_forward
- Which of the following statements cannot be supported by Kepler's laws of planetary motion? a The distance of a planet around the sun changes throughout its orbit. b The speed a planet is moving around the sun changes throughout the year. c The orbital period of Mercury can be calculated using the orbital period of Jupiter and the average distances of both planets. d The age of the four largest planets can be determined using the age of the four smallest planets and the average distances of each planet.arrow_forwardKepler’s First Law states that planetary orbits are ellipses with thesun at one focus. The orbit of Pluto has eccentricity e ≈ 0.25. Its perihelion (closest distance to the sun) is approximately 2.7 billion miles.Find the aphelion (farthest distance from the sun).arrow_forwardFor this problem the average distance of the earth from the sun is about 1.5×10^8km. Assume that the earth's orbit around the sun is circular and that the sun is at the origin of your coordinate system.arrow_forward
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