In November 2003, the now-most-distant-known object in the solar system was disc

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 an Sedna, is approximately 1700 km in diameter, takes about 1.05 times 10^4 years to orbit our sun, and reaches a maximum speed of 4.64 km/s. Calculations of its complete path, based upon several measurements of its position, indicate that its orbit is highly elliptical, varying from 76.0 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 km. What is Sedna's minimum speed? What is the ratio of Sedna's maximum kinetic energy to its minimum kinetic energy?

Explanation / Answer

A)
angular momentumL is conserved
L=Iw=Iv/r=mvr
v=L/(mr)
as L and m are constant the minimum speed v occurs when r=R [max distance from Sun]
L can be comupted knowing max speed V at minimum distance r from Sun
L=IV/r=mr^2V/R
then
v=V(r/R)
v=4.64(76/942) = 0.37 km/s

B) the ratio of maximum kinetic energy to minimum kinetic energy is
R=(K1/K2)^2 =

R=(V/v)^2
R=(4.64/0.37)^2 = 157.3

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