(a)
The semi-major axes of the orbits of the comets.
(a)
Answer to Problem 40QP
The semi-major axes of the comet Encke is
Explanation of Solution
The time period of the Earth around the sun is
The semi-major axis of a celestial body around the planet is almost equal to the average orbital distance of the body given by the Kepler’s law.
Write the expression for the Kepler’s third law for the comparison between the time period and orbital distance.
Here,
Conclusion:
For comet Encke:
Substitute
For comet Halley:
Substitute
For comet Hale-Bopp:
Substitute
Thus, the semi-major axes of the comet Encke is
(b)
The minimum and maximum distance of the comets Halley and Hale-Bopp from the sun.
(b)
Answer to Problem 40QP
The minimum and maximum distance of the comet Halley from the sun is
Explanation of Solution
The maximum and minimum distances reached by the comet from the sun in their orbits are termed as the Aphelion and Perihelion respectively.
Write the expression for the perihelion distance of the body in its orbit.
Here,
Write the expression for the aphelion distance of the body in its orbit.
Here,
Conclusion:
For Comet Halley:
Substitute
Substitute
For Comet Hale-Bopp:
Substitute
Substitute
Thus, the minimum and maximum distance of the comet Halley from the sun is
(c)
The region of origin of the comets Encke, Halley and Hale-Bopp in the solar system.
(c)
Answer to Problem 40QP
The Encke and Halley’s Comet are considered to be originated in the Kuiper belt whereas the Hale-Bopp comet is considered to be originated in Oort cloud region.
Explanation of Solution
The orbital time period of the comet suggests the region of origin of the Comet in the solar system. The comets that have a smaller time period are termed as the Short period comet and the one which have large time period are the long period comet.
The Encke comet has a very small time period of
The Halley comet is a short period comet with the time period of
Conclusion:
Thus, the Encke and Halley’s Comet are considered to be originated in the Kuiper belt whereas the Hale-Bopp comet is considered to be originated in Oort cloud region.
(d)
The comet which is the most and least pristine of the three.
(d)
Answer to Problem 40QP
The comet Encke is the least pristine and the comet Hale-Bopp is most pristine.
Explanation of Solution
As the comet comes close to the sun, the comet action takes place due to the sublimation of the ice and gases on the comet. This leads to the wear out of the material of the comet. The more the comet comes near the sun; more it loses its material.
The comet Encke is considered to be the least pristine as it has a very short time period and it encounters with the sun most frequently whereas the comet Hale-Bopp is considered to be the most pristine as it comes near the sun after a very long period.
Conclusion:
Thus, the comet Encke is the least pristine and the comet Hale-Bopp is most pristine.
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Chapter 12 Solutions
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