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Sedna: Solar System's Most Distant Object's Motion
Chapter 10, Problem 10.52(choose chapter or problem)
In November 2003, the now-most-distant-known object in the solar system was discovered by observation with a telescope on Mt. Palomar. This object known as Sedna, is approximately 1700 km in diameter, takes about 10,500 years to orbit our sun, and reaches a maximum speed of 4.64 km/s. Calculations of its complete path, based on several measurements of its position, indicate that its orbit is highly elliptical, varying from 76 AU to 942 AU in its distance from the sun, where AU is the astronomical unit, which is the average distance of the earth from the sun (\(1.50 \times 10^{8} \mathrm{~km}\)). (a) What is Sedna’s minimum speed? (b) At what points in its orbit do its maximum and minimum speeds occur? (c) What is the ratio of Sedna’s maximum kinetic energy to its minimum kinetic energy?
Questions & Answers
QUESTION:
In November 2003, the now-most-distant-known object in the solar system was discovered by observation with a telescope on Mt. Palomar. This object known as Sedna, is approximately 1700 km in diameter, takes about 10,500 years to orbit our sun, and reaches a maximum speed of 4.64 km/s. Calculations of its complete path, based on several measurements of its position, indicate that its orbit is highly elliptical, varying from 76 AU to 942 AU in its distance from the sun, where AU is the astronomical unit, which is the average distance of the earth from the sun (\(1.50 \times 10^{8} \mathrm{~km}\)). (a) What is Sedna’s minimum speed? (b) At what points in its orbit do its maximum and minimum speeds occur? (c) What is the ratio of Sedna’s maximum kinetic energy to its minimum kinetic energy?
ANSWER:
Step 1 of 5
We know that, the angular momentum of an object, \(\mathrm{L}=\mathrm{I} \omega\)
Where, I - moment of inertia of the object
\(\omega\) - Angular velocity of the object
We know that, \(\mathrm{I}=\mathrm{mr}^{2} \text { and } \omega=\mathrm{v} / \mathrm{r}\)
Where, v - linear velocity of the object and r - distance of center of mass.
Then, \(\mathrm{L}=m r^{2}(\mathrm{v} / \mathrm{r})\)
\(L=mrv\)
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Sedna: Solar System's Most Distant Object's Motion
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Journey to the outer reaches of our solar system with a captivating exploration of Sedna, the most distant-known object discovered in 2003. This enigmatic celestial body boasts a 1700 km diameter, a 10,500-year orbit around the sun, and a maximum speed of 4.64 km/s. Join us as we delve into the calculations of its elliptical orbit, its minimum speed, and the intriguing variations in its kinetic energy. Uncover the mysteries of Sedna's motion in this educational video.