Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Question
Chapter 14, Problem 50Q
(a)
To determine
The time period required to complete one orbit of Uranus by a particle in the epsilon ring of Uranus.
(b)
To determine
The direction in which the cloud appears to a person, when the person is riding on any particle in the epsilon ring and watching the cloud near the equator of Uranus.
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(a) What is the difference between the forces due to Uranus on a 1.0 kg mass located at the near side of Ariel and at the far side of Ariel? Ariel has a mean radius of 579 km and a mean orbital radius
about Uranus of 199,900 km. (Enter the magnitude in newtons.)
N
(b) Compare this difference to the difference for Earth due to the Moon, 0.22 × 10'
-5
N. (Tidal forces are the cause of volcanic activity on some moons.)
ΔF,
Ariel due to Uranus
ΔF.
Earth due to Moon
Calculate the Roche radius (in km) for Uranus. The diameter of Uranus is 5.11 ✕ 104 km.
Tutorial
Based on the orbital properties of Uranus, how far across the sky in arc seconds does it travel in one Earth
day? The average orbital radius is 2.88 x 109 km and the period is 84.0 years. (Assume Uranus and the Earth
are at the closest point to one another in their orbits.)
How many full Moons does this distance cover if the Moon has an angular diameter of 0.5 degrees?
Part 1 of 4
We first need to determine how fast the planet is moving across the sky. If we know the period and the
distance between the Sun and the planet we can calculate the velocity using:
2ar
which will tell us how many kilometers the planet travels in a day if we convert the period into days.
days
= (P
years'
|days/year
Pdays
days
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Chapter 14 Solutions
Universe
Ch. 14 - Prob. 1CCCh. 14 - Prob. 2CCCh. 14 - Prob. 3CCCh. 14 - Prob. 4CCCh. 14 - Prob. 5CCCh. 14 - Prob. 6CCCh. 14 - Prob. 7CCCh. 14 - Prob. 8CCCh. 14 - Prob. 9CCCh. 14 - Prob. 10CC
Ch. 14 - Prob. 11CCCh. 14 - Prob. 1QCh. 14 - Prob. 2QCh. 14 - Prob. 3QCh. 14 - Prob. 4QCh. 14 - Prob. 5QCh. 14 - Prob. 6QCh. 14 - Prob. 7QCh. 14 - Prob. 8QCh. 14 - Prob. 9QCh. 14 - Prob. 10QCh. 14 - Prob. 11QCh. 14 - Prob. 12QCh. 14 - Prob. 13QCh. 14 - Prob. 14QCh. 14 - Prob. 15QCh. 14 - Prob. 16QCh. 14 - Prob. 17QCh. 14 - Prob. 18QCh. 14 - Prob. 19QCh. 14 - Prob. 20QCh. 14 - Prob. 21QCh. 14 - Prob. 22QCh. 14 - Prob. 23QCh. 14 - Prob. 24QCh. 14 - Prob. 25QCh. 14 - Prob. 26QCh. 14 - Prob. 27QCh. 14 - Prob. 28QCh. 14 - Prob. 29QCh. 14 - Prob. 30QCh. 14 - Prob. 31QCh. 14 - Prob. 32QCh. 14 - Prob. 34QCh. 14 - Prob. 35QCh. 14 - Prob. 36QCh. 14 - Prob. 37QCh. 14 - Prob. 38QCh. 14 - Prob. 39QCh. 14 - Prob. 40QCh. 14 - Prob. 41QCh. 14 - Prob. 42QCh. 14 - Prob. 43QCh. 14 - Prob. 44QCh. 14 - Prob. 45QCh. 14 - Prob. 46QCh. 14 - Prob. 48QCh. 14 - Prob. 49QCh. 14 - Prob. 50QCh. 14 - Prob. 51QCh. 14 - Prob. 52QCh. 14 - Prob. 53QCh. 14 - Prob. 54QCh. 14 - Prob. 55QCh. 14 - Prob. 56QCh. 14 - Prob. 57QCh. 14 - Prob. 58QCh. 14 - Prob. 59Q
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- Does Uranus have enough mass to have formed by gravitational collapse? How do you know?arrow_forwardWhat is the consequence of Uranus’ spin axis being 98° away from perpendicular to its orbital plane?arrow_forwardOne way to recognize a distant planet is by studying the planet’s motion along its orbit. If Uranus circles the Sun in 84.0 years, how many arc seconds will it move in 1 earth day? Assume a circular orbit for Uranus, and pretend that earth is not moving.arrow_forward
- (a) Auroras have been observed near the magnetic poles of Uranus. (i) Explain how these lights are produced. (ii) While searching for the auroras of Uranus, an orbiting satellite registered the spectral lines. These are emitted by hydrogen atoms during the transition from the first excited state to the ground state. Calculate the wavelength of this radiation and indicate the region of the electromagnetic spectrum in which the satellite made the observation.arrow_forwardIn Neptune's rings, each ring particle collides with another particle on average around every 8.7 hours. If a ring particle was to survive for the age of the solar system, which is 4.6 x109 years, how many collisions would it undergo? Assume there are 365.25 days in a yeararrow_forwardThe mean diameter of Uranus is 50,724 km. The planet has a mean mass density of 1.27g/cm^3. What is the acceleration due to gravity at Uranus' surface?arrow_forward
- Uranus is about 26,000 km in radius, and its main ring is about 51,000 km from the planets center. If you represent the planet with a ball 5 inches in radius, how far from the center would you place its main ring?arrow_forwardDescribe four differences between the two ice giants, Uranus and Neptune, and the two gas giants, Jupiter and Saturn. (Hint: Review Celestial Profiles for all of these planets.)arrow_forward) The diameter of the moon is about 11 million feet, and the diameter of Uranus is about170 million feet. If a scale model of the solar system is constructed so that the diameter of the moonis 1.2 feet, what will be the diameter of Uranus in feetarrow_forward
- Consider the attached light curve for a transiting planet observed by the Kepler mission. If the host star is identical to the sun, what is the radius of this planet? Give your answer in terms of the radius of Jupiter. Brightness of Star Residual Flux 0.99 0.98 0.97 0.006 0.002 0.000 -8-881 -0.06 -0.04 -0.02 0.00 Time (days) → 0.02 0.04 0.06arrow_forward(a) What is the difference between the forces due to Neptune on a 1.0 kg mass located at the near side of Triton and at the far side of Triton? Triton has a mean radius of 1,353 km and a mean orbital radius about Neptune of 354,800 km. (Enter the magnitude in newtons.) N (b) Compare this difference to the difference for Earth due to the Moon, 0.22 x 10- N. (Tidal forces are the cause of volcanic activity on some moons.) AFTriton due to Neptune AF Earth due to Moonarrow_forwardGM What is the orbital velocity and period of a ring particle at the outer edge of Saturn's A ring? (Note: The radius of the edge of the A ring is 136,500 km. Hint: Use the formula for orbital velocity, V. = v orbital velocity km/s period hrarrow_forward
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