Given that global warming has gone haywire, nuclear power offers a potential sol

Question

Given that global warming has gone haywire, nuclear power offers a potential solution, but nobody wants unclear waste in their backyard. A group of keen ASP2062 students hatch a plan to dispose of nuclear waste by accreting it onto the Sun. a) Estimate the energy required to land 1kg of waste on the Sun, having already been jettisoned from the Earth, by removing all of the angular momentum given to the package by Earth's orbit (Fig. 1a). b) Estimate the energy required to land the same radioactive turd-ball on the Moon (plan b: distance to the moon is 384.400 km: see Fig. 1b). c) How much more energy is required to land the waste on the Sun compared to landing it on the Moon?

Explanation / Answer

A) In order to land it on the Sun, all the energy it is having should be reduced to zero, so using the relation Energy = L2/2I, where L is the angular momentum, and I is moment of inertia,

Now angular momentum L= mvr = m(gr)r,

r = 1 AU = 1.5 x 108 km = 1.5 x 1011 m and g = 9.8 m/s2

And moment of inertia I = mr2

so energy = {m(GM/r)r}2/2mr2 = m2 GM/2mr =mGM/2r

Where M is mass of Sun and G is universal gravitational constant

Energy = (1 x 6.6 x 10-34 x 1.98 x 1030 )/2 x 1.5 x 1011

   = 4.36 x 10-15 Joules

B) now in case of moon, we have to manage the waste to start revolving around earth in the orbit of moon.

so energy of orbiting waste = 1/2 mv2 = m(GM/r)2/2

Energy = mGM/2r = 1 x 6.6 x 10-34 x 5.97 x 1024/2 x 3.84 x 108

   So energy = 5.13 x 10-18 Joules

C) difference in energy = (4.36 - 0.00513) x 10-15 joules

   = 4.35 x 10-15 joules

  

  

A

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