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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A new planet Batuu is discovered in our solar system. Observations reveal that the orbital period of Batuuis TBatuu = 120 Earth days and its diameter is dBatuu = 12 × 106 m. Astronauts are sent in a rocket toexplore the planet further
how far is planet batuu from the sun?
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).
Show 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.
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_forwardA 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 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
- A 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_forwardThe mean distance of Mars from the Sun is 1.52 times that of Earth from the Sun. From Kepler’s law of periods, calculate the number of years required for Mars to make one revolution around the Sun; compare your answer with the value given in Appendix C.arrow_forwardAstronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 • 1011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0 • 104 light years from its center. What should the orbital period of that star be in years? Part (b) If its period is 6.0 • 107 years instead, what is the mass of the galaxy in solar masses? Such calculations are used to imply the existence of “dark matter” in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.arrow_forward
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