Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 7, Problem 11PQ
To determine
The travel time to moon.
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The ratio of the radius of the earth to that
of the moon is 10. The ratio of acceleration due
to gravity on the earth to the moon is 6. The
ratio of escape velocity from earth's surface to
that of moon is.
(a) 10
(b) 6
(c) 1.66
(d) 7.74
(a) Based on the observations, determine the total mass M of the planet.
(b) Which moon and planet of our solar system is the team observing? (Use literature.)
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).
Chapter 7 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 7.1 - What important experimental skills can we learn...Ch. 7.2 - Three possible planetary orbits are shown in...Ch. 7.2 - Prob. 7.3CECh. 7.2 - Prob. 7.4CECh. 7.2 - Todays employees are rewarded for thinking outside...Ch. 7 - We use the terms sunset and sunrise. In what way...Ch. 7 - Prob. 2PQCh. 7 - For many years, astronomer Percival Lowell...Ch. 7 - Prob. 4PQCh. 7 - Prob. 5PQ
Ch. 7 - Io and Europa are two of Jupiters many moons. The...Ch. 7 - Model the Moons orbit around the Earth as an...Ch. 7 - Prob. 8PQCh. 7 - Prob. 9PQCh. 7 - Prob. 10PQCh. 7 - Prob. 11PQCh. 7 - Prob. 12PQCh. 7 - A massive black hole is believed to exist at the...Ch. 7 - Since 1995, hundreds of extrasolar planets have...Ch. 7 - When Sedna was discovered in 2003, it was the most...Ch. 7 - Prob. 16PQCh. 7 - The mass of the Earth is approximately 5.98 1024...Ch. 7 - Prob. 18PQCh. 7 - Prob. 19PQCh. 7 - A black hole is an object with mass, but no...Ch. 7 - Prob. 21PQCh. 7 - Prob. 22PQCh. 7 - The Lunar Reconnaissance Orbiter (LRO), with mass...Ch. 7 - A Suppose a planet with mass m is orbiting star...Ch. 7 - Prob. 25PQCh. 7 - Three billiard balls, the two-ball, the four-ball,...Ch. 7 - Saturns ring system forms a relatively thin,...Ch. 7 - Prob. 28PQCh. 7 - Find the magnitude of the Suns gravitational force...Ch. 7 - Prob. 30PQCh. 7 - Prob. 31PQCh. 7 - Prob. 32PQCh. 7 - Prob. 33PQCh. 7 - Prob. 34PQCh. 7 - Prob. 35PQCh. 7 - In your own words, describe the difference between...Ch. 7 - The Sun has a mass of approximately 1.99 1030 kg....Ch. 7 - Prob. 38PQCh. 7 - Prob. 39PQCh. 7 - Prob. 40PQCh. 7 - Three billiard balls, the two-ball, the four-ball,...Ch. 7 - Prob. 42PQCh. 7 - Prob. 43PQCh. 7 - Prob. 44PQCh. 7 - Figure P7.45 shows a picture of American astronaut...Ch. 7 - Prob. 46PQCh. 7 - Prob. 47PQCh. 7 - Prob. 48PQCh. 7 - Prob. 49PQCh. 7 - Prob. 50PQCh. 7 - The International Space Station (ISS) experiences...Ch. 7 - Prob. 52PQCh. 7 - Two black holes (the remains of exploded stars),...Ch. 7 - Prob. 54PQCh. 7 - Prob. 55PQCh. 7 - Consider the Earth and the Moon as a two-particle...Ch. 7 - Prob. 57PQCh. 7 - Consider the Earth and the Moon as a two-particle...Ch. 7 - Prob. 59PQCh. 7 - You are a planetary scientist studying the...Ch. 7 - Prob. 61PQCh. 7 - Prob. 62PQCh. 7 - Planetary orbits are often approximated as uniform...Ch. 7 - Prob. 64PQCh. 7 - Prob. 65PQCh. 7 - Prob. 66PQCh. 7 - Prob. 67PQCh. 7 - Prob. 68PQCh. 7 - Prob. 69PQCh. 7 - Prob. 70PQ
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- Let 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_forwardCalculate the effective gravitational field vector g at Earths surface at the poles and the equator. Take account of the difference in the equatorial (6378 km) and polar (6357 km) radius as well as the centrifugal force. How well does the result agree with the difference calculated with the result g = 9.780356[1 + 0.0052885 sin 2 0.0000059 sin2(2)]m/s2 where is the latitude?arrow_forwardWhat is the orbital radius of an Earth satellite having a period of 1.00 h? (b) What is unreasonable about this result?arrow_forward
- The “mean” orbital radius listed for astronomical objects orbiting the Sun is typically not an integrated average but is calculated such that it gives the correct period when applied to the equation for circular orbits. Given that, what is the mean orbital radius in terms of aphelion and perihelion?arrow_forwardOn a planet whose radius is 1.2107m , the acceleration due to gravity is 18m/s2 . What is the mass of the planet?arrow_forwardSuppose 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_forward
- If a planet with 1.5 times the mass of Earth was traveling in Earth’s orbit, what would its period be?arrow_forwardKepler's third law states that for any object in a gravitational orbit, P2∝a3P2∝a3 where PP is the orbital period of the object and aa is the average distance between the object and what it is orbiting. In our Solar System, the natural units are distances measured in astronomical units (A.U.) and orbital periods measured in years. This can be seen for the Earth-Sun system which has an orbital period P=1P=1 year and an average distance a=1a=1 AU. Using these natural units in the Solar System, the proportionality becomes an equality, so for our Solar System: (Pyears)2=(aA.U.)3(Pyears)2=(aA.U.)3 . Using your mathematical prowess, determine what the orbital period in years would be for an asteroid that was discovered orbiting the Sun with an average distance of 25 astronomical units.arrow_forwardShow that the radius r of the orbit of a moon of a given planet can be determined from the radius R of the planet, the acceleration of gravity at the surface of the planet, and the time τ required by the moon to complete one full revolution about the planet. Determine the acceleration of gravity at the surface of the planet Jupiter knowing that R = 71 492 km and that τ = 3.551 days and r= 670.9 × 103 km for its moon Europa.arrow_forward
- A spacecraft is in an elliptical orbit around the earth. At th etime t = 0 hours, it is at its apogee (highest point), 1000 km above the earth's surface. It is at its perigee (lowest point), 100 km above the surface 50 minutes later. Assuming that distance from the earth varies sinusoidally with time, write an equation and find the first 3 positive values of t for which the spacecraft is 200 km from the surface.arrow_forwardA satellite travels with constant speed v in a circular orbit 320 km above the earth’s surface. Calculate v knowing that the acceleration of the satellite is the gravitational acceleration at its altitude. (Note: Review Art. 1/5 as necessary and use the mean value of g and the mean value of the earth’s radius. Also recognize that v is the magnitude of the velocity of the satellite with respect to the center of the earth.)arrow_forwardA communication satellite in geosynchronous orbit remains above a single point on the Earth's equator as the planet rotates on its axis. (a) Calculate the radius of its orbit. (b) The satellite relays a radio signal from a transmitter near the North Pole to a receiver, also near the North Pole. Traveling at the speed of light, how long is the radio wave in transit?arrow_forward
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