EBK UNDERSTANDING OUR UNIVERSE (THIRD E
3rd Edition
ISBN: 9780393631760
Author: Blumenthal
Publisher: VST
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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.
What is Kepler's first law of
planetary motion?
The period of a planet's
orbit is proportional to
its distance from the
sun.
Planets have circular
orbits.
Planets have elliptical
orbits.
The eccentricity of a
planet's orbit is
proportional to its
distance from the sun.
Chapter 3 Solutions
EBK UNDERSTANDING OUR UNIVERSE (THIRD E
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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- 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.arrow_forwardConsider the Earth's orbit around the Sun to be circular with radius R = 9.30 x 107 mi and it takes 365 days to complete one revolution. What is the distance Earth traveled for one revolution (circumference of a circle is 2??2πR )?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
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- 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_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_forwardNeptune 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_forward
- Suppose 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_forwardYou are planning a dream vacation to Mars. For the orbital dynamics part of the vacation planning assume that Earth is in a circular orbit 1.00 AU from the Sun and Mars is in a circular orbit 1.52 AU from the Sun. Assume the the orbits of Earth and Mars are coplanar and that they go around the Sun the same way. The orbit you plan to use for your trip is an ellipse with the Sun at one focus (Kepler's 1st Law). The perihelion of the ellipse is at Earth's orbit at 1.00 AU and the aphelion is at Mars' orbit at 1.52 AU. Your spacecraft will go around the Sun in the same sense as Earth and Mars. The orbit you have chosen is called a Hohmann Transfer Orbit. A. What is the semi-major axis a of the spacecraft's orbit? What is the eccentricity of the spacecraft's orbit? B. What is the orbital period of the spacecraft? How long does it take to get to Mars? How long does it take to get back? C. When (at what Earth - Mars configuration) do you launch to go? In other words, where does Mars need to…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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