Physics for Science and Engineering With Modern Physics, VI - Student Study Guide
4th Edition
ISBN: 9780132273244
Author: Doug Giancoli
Publisher: PEARSON
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Chapter 6, Problem 61GP
To determine
The mass of SgrA in
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Astronomers have observed an otherwise normal star, called S2, closely orbiting an extremely massive but small object at the center of the Milky Way Galaxy called SgrA. S2 moves in an elliptical orbit around SgrA with a period of 15.2 yr and an eccentricity ee = 0.87. In 2002, S2 reached its closest approach to SgrA, a distance of only 123 AU (1AUAU = 1.50×1011m1.50×1011m is the mean Earth - Sun distance).
Determine the mass MM of SgrA, the massive compact object (believed to be a supermassive black hole) at the center of our Galaxy. State MM in kgkg and in terms of the mass of our Sun.
Express your answer using two significant figures.
A planet of mass ?=5.45×10^24 kg is orbiting in a circular path a star of mass ?=4.45×10^29 k . The radius of the orbit is ?=8.35×107^7km.
What is the orbital period (in Earth days) of the planet ?planet?
Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 ✕ 1011 solar masses. A star orbiting near the galaxy's periphery is 6.0 ✕ 104 light years from its center.
What should the orbital period (in y) of that star be?
Chapter 6 Solutions
Physics for Science and Engineering With Modern Physics, VI - Student Study Guide
Ch. 6.3 - Suppose you could double the mass of a planet but...Ch. 6.4 - Two satellites orbit the Earth in circular orbits...Ch. 6.4 - Could astronauts in a spacecraft far out in space...Ch. 6.5 - Suppose there were a planet in circular orbit...Ch. 6 - Does an apple exert a gravitational force on the...Ch. 6 - The Suns gravitational pull on the Earth is much...Ch. 6 - Will an object weigh more at the equator or at the...Ch. 6 - Why is more fuel required for a spacecraft to...Ch. 6 - The gravitational force on the Moon due to the...Ch. 6 - How did the scientists of Newton's era determine...
Ch. 6 - If it were possible to drill a hole all the way...Ch. 6 - A satellite in a geosynchronous orbit stays over...Ch. 6 - Which pulls harder gravitationally, the Earth on...Ch. 6 - Would it require less speed to launch a satellite...Ch. 6 - An antenna loosens and becomes detached from a...Ch. 6 - Describe how careful measurements of the variation...Ch. 6 - The Sun is below us at midnight, nearly in line...Ch. 6 - When will your apparent weight be the greatest, as...Ch. 6 - If the Earths mass were double what it actually...Ch. 6 - The source of the Mississippi River is closer to...Ch. 6 - People sometimes ask. What keeps a satellite up in...Ch. 6 - Explain how a runner experiences free fall or...Ch. 6 - If you were in a satellite orbiting the Earth, how...Ch. 6 - Is the centripetal acceleration of Mars in its...Ch. 6 - The mass of the planet Pluto was not known until...Ch. 6 - The Earth moves faster in its orbit around the Sun...Ch. 6 - Keplers laws tell us that a planet moves faster...Ch. 6 - Does your body directly sense a gravitational...Ch. 6 - Discuss the conceptual differences between g as...Ch. 6 - (I) Calculate the force of Earths gravity on a...Ch. 6 - (I) Calculate the acceleration due to gravity on...Ch. 6 - Prob. 3PCh. 6 - Prob. 4PCh. 6 - Prob. 5PCh. 6 - (II) Calculate the effective value of g, the...Ch. 6 - (II) You are explaining to friends why astronauts...Ch. 6 - Prob. 8PCh. 6 - (II) Four 8.5-kg spheres are located at the...Ch. 6 - (II) Two objects attract each other...Ch. 6 - (II) Four masses are arranged as shown in Fig....Ch. 6 - (II) Estimate the acceleration due to gravity at...Ch. 6 - (II) Suppose the mass of the Earth were doubled,...Ch. 6 - Prob. 14PCh. 6 - (II) At what distance from the Earth will a...Ch. 6 - (II) Determine the mass of the Sun using the known...Ch. 6 - (II) Two identical point masses, each of mass M,...Ch. 6 - Prob. 18PCh. 6 - (III) (a) Use the binomial expansion...Ch. 6 - Prob. 20PCh. 6 - Prob. 21PCh. 6 - Prob. 22PCh. 6 - Prob. 23PCh. 6 - Prob. 24PCh. 6 - (II) You know your mass is 65 kg, but when you...Ch. 6 - (II) A 13.0-kg monkey hangs from a cord suspended...Ch. 6 - (II) Calculate the period of a satellite orbiting...Ch. 6 - Prob. 28PCh. 6 - (II) What will a spring scale read for the weight...Ch. 6 - Prob. 30PCh. 6 - (II) What is the apparent weight of a 75-kg...Ch. 6 - (II) A Ferris wheel 22.0 m in diameter rotates...Ch. 6 - Prob. 33PCh. 6 - Prob. 34PCh. 6 - Prob. 35PCh. 6 - (III) An inclined plane, fixed to the inside of an...Ch. 6 - (I) Use Keplers laws and the period of the Moon...Ch. 6 - (I) Determine the mass of the Earth from the known...Ch. 6 - (I) Neptune is an average distance of 4.5109 km...Ch. 6 - (II) Planet A and planet B are in circular orbits...Ch. 6 - (II) Our Sun rotates about the center of our...Ch. 6 - (II) Table 63 gives the mean distance, period, and...Ch. 6 - (II) Determine the mean distance from Jupiter for...Ch. 6 - (II) The asteroid belt between Mars and Jupiter...Ch. 6 - (III) The comet Hale-Bopp has a period of 2400...Ch. 6 - Prob. 46PCh. 6 - (III) The orbital periods and mean orbital...Ch. 6 - (II) What is the magnitude and direction of the...Ch. 6 - (II) (a) What is the gravitational field at the...Ch. 6 - Prob. 50PCh. 6 - How far above the Earths surface will the...Ch. 6 - At the surface of a certain planet, the...Ch. 6 - A certain white dwarf star was once an average...Ch. 6 - What is the distance from the Earths center to a...Ch. 6 - The rings of Saturn are composed of chunks of ice...Ch. 6 - During an Apollo lunar landing mission, the...Ch. 6 - Prob. 57GPCh. 6 - Prob. 58GPCh. 6 - Jupiter is about 320 limes as massive as the...Ch. 6 - The Sun rotates about the center of the Milky Way...Ch. 6 - Prob. 61GPCh. 6 - A satellite of mass 5500 kg orbits the Earth and...Ch. 6 - Show that the rate of change of your weight is...Ch. 6 - Astronomers using the Hubble Space Telescope...Ch. 6 - Suppose all the mass of the Earth were compacted...Ch. 6 - A plumb bob (a mass m hanging on a string) is...Ch. 6 - A geologist searching for oil finds that the...Ch. 6 - Prob. 68GPCh. 6 - A science-fiction tale describes an artificial...Ch. 6 - How long would a day be if the Earth were rotating...Ch. 6 - An asteroid of mass m is in a circular orbit of...Ch. 6 - Newton had the data listed in Table 64, plus the...Ch. 6 - A satellite circles a spherical planet of unknown...Ch. 6 - Prob. 74GPCh. 6 - The gravitational force at different places on...Ch. 6 - Prob. 76GPCh. 6 - Estimate the value of the gravitational constant G...Ch. 6 - Between the orbits of Mars and Jupiter, several...
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- An object of mass mm is launched from a planet of mass M and radius R. Calculate this minimum launch speed (called the escape speed), in meters per second, for a planet of mass M=5.38×1023kg and R=83.2×103km. V= ( 2 G M/R )0.5=arrow_forwardAn object of mass mm is launched from a planet of mass MM and radius RR. a) Derive and enter an expression for the minimum launch speed needed for the object to escape gravity, i.e. to be able to just reach r=∞. b) Calculate this minimum launch speed (called the escape speed), in meters per second, for a planet of mass M=2.73×1023kg and R=86.2×103km.arrow_forward(a) At what position in its elliptical orbit is the speed of a planet a maximum? when it is closest to the sun when it is farthest from the sun when it is midway between its farthest and closest distances to the sun everywhere in its orbit, the speed is constant (b) At what position is the speed a minimum? when it is closest to the sun when it is farthest from the sun when it is midway between its farthest and closest distances to the sun everywhere in its orbit, the speed is constantarrow_forward
- An object of mass m is launched from a planet of mass M and radius R. Calculate this minimum launch speed (called the escape speed), in meters per second, for a planet of mass M = 2 × 1023 kg and R = 78 × 102 km.arrow_forwardA planet with a mass of 3.0 x 1023kg orbits 6.0 x 1010m from a star with a period of 2.2 x 1011seconds. Determine the mass of the star. Enter you answer using E notation.arrow_forwardA planet of mass ?=5.45×10^24 kg is orbiting in a circular path a star of mass ?=4.45×10^29 kg . The radius of the orbit is ?=8.35×10^7 km. What is the orbital period (in Earth days) of the planet ?planet ?arrow_forward
- Two celestial bodies whose masses are m1 and m2 are revolving around their common center of mass and the distance between them is L. Assuming that they are both point masses, Find the angular speed, tangential speeds of the masses m1 and m2, and period of the motion. Universal Gravitational Constant, G=6,6742867E-11 m3 kg / s2(Note that the exponent is negative)Radius of Earth, RE: 6,3781366E+06 mMass of Earth, ME: 5,9721426E+24 kg m1=10^12kg m2=10^11kg L=10^8m 7,27210E+00 m1 3,85280E+00 m2 6,16500E+00 Larrow_forward(c) In the case of a binary-star system, with stars of mass my and m2 separated by a distance r, the period, T, of the system is given by T²= (d) D 472 Show from first principles that di, the orbital radius of the star of mass mi, is given by G (m₁+ m₂) +3 d₁=m₂ GT² 4π² (m₁ + m₂) ² ³arrow_forwardUse a distance of R = 1.48x10^11 meters for the distance between the earth and the sun. Use a mass of 1.99x10^30 kg to be 1 solar mass. For each of the different sun masses (as values of solar mass, aka 0.5 solar masses = 1x10^30 kg), as outlined in the lecture, calculate the period of the earth's orbit in days using Kepler's law for circular orbits (I double-checked it with these values and it works) and also calculate the corresponding orbital velocity of the earth. Questions: 1.) Using these values, and 6x10^24 kg for the mass of the earth, what is the strength of the gravitational force between the earth and the sun? 2.) If the earth were twice as far from the sun, what would be its period of orbit? 3.) Mars orbits the sun at a distance of 2.18x10^11 meters. How long is a Martian year, using Kepler's law for circular orbits?arrow_forward
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