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 15.2, Problem 15.2CYU
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A non-rotating black hole has an ‘edge’ at what’s called it’s Schwartzschildradius. For a black hole of mass M, the Schwartzschild radius isRSch = 2GM/(c^2) where G is the gravitational constant and c is the speed of light. Close to black holes, we really should use Einstein’s theory of gravity (General Relativity) instead of Newton’s, but Newton’s is still a good approximation.Using Newtonian Gravity, find the gravitational force on a mass m at theSchwartzschild radius of a black hole. (Your answer for this should look likeFgrav = an expression in terms of G, M, m, c and numbers.) Is the forcesmaller or larger for a more massive black hole?
A star near the visible edge of a galaxy travels in a uniform circular orbit. It is 43,500 ly (light-years) from the galactic center and has a speed of 275 km/s.
a.)Estimate the total mass of the galaxy based on the motion of the star. Gravitational constant is 6.674×10−11m3/(kg·s2) and mass of the Sun Ms=1.99 × 1030 kg.
b.)The total visible mass (i.e., matter we can detect via electromagnetic radiation) of the galaxy is 1011 solar masses. What fraction of the total mass of the galaxy is visible, according to this estimate?
The rate at which a nebular cloud rotates increases as the cloud collapses to form systems of stars and planets. Consider a small
segment of a nebular cloud with a mass m of 1.9 x 1027 kg, tangential velocity vinitial equal to 6.8 km s¯1 located at an orbital
distance rinitial = 2.5 x 104 km. After the cloud collapses, the same small segment is located at an orbital distance
rinal = 3.2 x 10° km. Calculate the change of the rotational velocity, Ao, for the cloud segment, assuming perfectly circular
orbits. Perform your work and report your solution using two significant figures.
Δω-
rad s-
Chapter 15 Solutions
Understanding Our Universe
Ch. 15.1 - Prob. 15.1CYUCh. 15.2 - Prob. 15.2CYUCh. 15.3 - Prob. 15.3CYUCh. 15.4 - Prob. 15.4CYUCh. 15 - Prob. 1QAPCh. 15 - Prob. 2QAPCh. 15 - Prob. 3QAPCh. 15 - Prob. 4QAPCh. 15 - Prob. 5QAPCh. 15 - Prob. 6QAP
Ch. 15 - Prob. 7QAPCh. 15 - Prob. 8QAPCh. 15 - Prob. 9QAPCh. 15 - Prob. 10QAPCh. 15 - Prob. 11QAPCh. 15 - Prob. 12QAPCh. 15 - Prob. 13QAPCh. 15 - Prob. 14QAPCh. 15 - Prob. 15QAPCh. 15 - Prob. 16QAPCh. 15 - Prob. 17QAPCh. 15 - Prob. 18QAPCh. 15 - Prob. 19QAPCh. 15 - Prob. 20QAPCh. 15 - Prob. 21QAPCh. 15 - Prob. 22QAPCh. 15 - Prob. 23QAPCh. 15 - Prob. 24QAPCh. 15 - Prob. 25QAPCh. 15 - Prob. 26QAPCh. 15 - Prob. 27QAPCh. 15 - Prob. 28QAPCh. 15 - Prob. 29QAPCh. 15 - Prob. 30QAPCh. 15 - Prob. 31QAPCh. 15 - Prob. 32QAPCh. 15 - Prob. 33QAPCh. 15 - Prob. 34QAPCh. 15 - Prob. 35QAPCh. 15 - Prob. 36QAPCh. 15 - Prob. 37QAPCh. 15 - Prob. 38QAPCh. 15 - Prob. 39QAPCh. 15 - Prob. 40QAPCh. 15 - Prob. 41QAPCh. 15 - Prob. 42QAPCh. 15 - Prob. 43QAPCh. 15 - Prob. 44QAPCh. 15 - Prob. 45QAP
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- A hypothetical planet has a radius 2.0 times that of earth , but has the same mass , what is the acceleration due to gravity near it's surface , gplanet = ?arrow_forwardNeptune has a mass of 1.0 ✕ 1026 kg and is 4.5 ✕ 109 km from the Sun with an orbital period of 165 years. Planetesimals in the outer primordial solar system 4.5 billion years ago coalesced into Neptune over hundreds of millions of years. If the primordial disk that evolved into our present day solar system had a radius of 1011 km, and if the matter that made up these planetesimals that later became Neptune was spread out evenly on the edges of it, what was the orbital period (in years) of the outer edges of the primordial disk? yrarrow_forwardNeptune has a mass of 1.0 ✕ 1026 kg and is 4.5 ✕ 109 km from the Sun with an orbital period of 165 years. Planetesimals in the outer primordial solar system 4.5 billion years ago coalesced into Neptune over hundreds of millions of years. If the primordial disk that evolved into our present day solar system had a radius of 1011 km, and if the matter that made up these planetesimals that later became Neptune was spread out evenly on the edges of it, what was the orbital period (in years) of the outer edges of the primordial disk?arrow_forward
- The Earth’s radius is about 6400 km. The International Space Station (ISS) orbits about 400 km above Earth’s surface. So the center-to-center distance between Earth’s center and the space station is about 6800 km. Estimate Earth’s gravitational acceleration at the space station orbital height, giss. Use the ratio approach: giss / g = giss /980 = (6400 /6800)^2 = giss = cm/s^2.arrow_forwardNeptune has a mass of 1.0 × 1026 kg and is 4.5 × 10⁹ km from the Sun with an orbital period of 177.5 years. Planetesimals in the outer primordial solar system 4.5 billion years ago coalesced into Neptune over hundreds of millions of years. If the primordial disk that evolved into our present day solar system had a radius of 10¹1 km and if the matter that made up these planetesimals that later became Neptune was spread out evenly on the edges of it, what was the orbital period of the outer edges of the primordial disk? Express your answer rounded to the nearest year, and be sure not to do any rounding before expressing your final answer. P = yearsarrow_forwardWhat is the Schwarzschild radius for the black hole at the center of our galaxy if it has the mass of 4 million solar masses?arrow_forward
- What is the orbital velocity of our solar system about the center of the MilkyWay? Assume that the mass within a sphere of radius equal to our distance away from the center is about a 100 billion solar masses. Our distance from the center is 27,000 light years.arrow_forwardA star near the visible edge of a galaxy travels in a uniform circular orbit. It is 48,300 ly (light-years) from the galactic center and has a speed of 275 km/s. Estimate the total mass of the galaxy based on the motion of the star. Gravitational constant is 6.674×10−11 m3/(kg·s2) and mass of the Sun Ms=1.99 × 1030 kg. dont provide hand written solutionarrow_forward29. In a planetary system, p-h-y- s-i-c-x, located on the Milktea Way galaxy, seven iden- tical planets with mass m were observed which follows the configuration shown in the figure. Assuming that the given distances are from the center of each planet, what is the magnitude of the net gravitational force on planet y due to all the masses? a A. (3 - *) B. (3 + 4) Gm? 2Gm? a Gm² a2 D. 3Gm? a2arrow_forward
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