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 23QAP
To determine
The fundamental difference between Kepler’s law and Newton’s law.
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Newton’s law of gravitation and the formula for centripetal acceleration can be used to show that:
T^2=(4π^2/Gms)R^3 where G is the universal constant of gravitation and MS is the mass of the Sun. Take logarithms to base 10 of both sides of the equation to complete the expression for 2 lg T.2 lg T = ……………… × lg R + ……………………
Kepler's 1st law says that our Solar System's planets orbit in ellipses around the Sun where the closest distance to the Sun is called perihelion.
Suppose I tell you that there is a planet with a perihelion distance of 2 AU and a semi-major axis of 1.5 AU.
Does this make physical sense? Explain why or why not.
Which of the following statements is supported by Kepler's laws of planetary motion?
Earth orbits the Sun at a constant speed, never speeding up or slowing down.
Earth's orbit is a perfect circle, with the Sun located at the center of the circle.
Earth orbits the Sun at a slightly faster speed every year.
Earth has an elliptical orbit, with the Sun located at one focus of the ellipse.
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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- The Halley’s Comet regularly passes by the earth on its tour around the sun (at the time of Jesus’ birth itwas something different, most probably). The semi-major axis of the elliptical path is 17.8 AU(astronomical unit = 150·109 m). Halley’s last visit at our earth was in 1985. Are you going to experience the next visit?arrow_forwardSam is an astronomer on planet Hua, which orbits the distant star Barnard. It has recently been accepted that Hua is spherical in shape, although its exact size is unknown. While studying in the library, in the city of Joy, Sam learns that during equinox, Barnard is directly overhead in the city of Bar, located 1500.0 km north of his location. On the equinox, Sam goes outside and measures the altitude of Barnard at 83 degrees. What is the radius of Hua in km?arrow_forwardTwo exoplanets, UCF1.01 and UCF1.02 are found revolving around the same star. The period of planet UCF1.01 is 92.4 days, and that of planet UCF1.02 is 7.1 days. If the average distance of UCF1.01 to the sun is 5,828.0 km, what is the average distance of UCF1.02 to the sun in km? Please keep four digits after decimal points.arrow_forward
- A planet is about 7.79 x 108 km (orbital radius) from the sun. It takes 1,425 days for the planet to go around its orbit (assume circular orbit). What is the orbital velocity in km/sec of the planet along its orbital path? What is its acceleration toward the sun in km/sec2? (Force attraction of sun = ma = mv2); r = orbital radius rarrow_forwardQuestion 4: Use Kepler's 3rd law to find the orbital periods (assume circular orbits) for the inner planets given that their orbital radii are: Mercury: 5.8 x 107 km Venus: 1.08 x 108 kmarrow_forwardMars has an orbital radius of 1.523 AU and an orbital period of 687.0 days. What is its average speed v in SI units? (1 AU is the astronomical unit, the mean distance between the Sun and the Earth, which is 1.496×1011 m) a. 0.00221 AU/day b. 3838 m/s c. 0 d. 1.28×10−9 m/sarrow_forward
- Neptune orbits the Sun with an orbital radius of 4.495 x 10^12 m. If the earth to sun distance 1A.U. = 1.5 x 10^11 m, a) Determine how many A.U.'s is Neptune's orbital radius (Round to the nearest tenth). b) Given the Sun's mass is 1.99 x10^30 kg, use Newton's modified version of Kepler's formula T^2 = (4pi^2/Gm(star)) x d^3 to find the period in seconds using scientific notation. (Round to the nearest thousandth). C) Convert the period in part b) to years (Round to the nearest tenth)arrow_forwardSuppose humans are successful in living on the moon. They would need GPS just like on Earth to be able to navigate to “Moonmart”. They launch a 500 kg satellite in a geosynchronous orbit around the moon. Assume the Moon’s mass is 7.35x1022 kg.The moon takes 708.7 hours to make 1 rotation, or 2,551,320 seconds. What is the satellite’s orbit radius? What is the satellite’s orbit speed? After 20 years, a newer GPS satellite is built, and they want to get rid of the old one. How much energy is needed for the original satellite to escape its moon orbit?arrow_forwardA planet of mass m= 8.45 x 1024 kg is orbiting in a circular path a star of mass M= 6.95 x 1029 kg. The radius of the orbit is R= 3.15 x 107km. What is the orbital pperiod (in Earth days) of the planet Pplanet? Express your answer to three significant figures. Pplanet = ? daysarrow_forward
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