Work done by the Sun on the Earth

Classical Mechanics Level 2

The Earth takes 1 year to complete its orbit around the Sun. Treating the orbit as perfectly circular, find the net work done on the Earth by the Sun in $\frac14$ of a year. Give your answer to three significant figures.

Assumptions:

Mass of the Earth = $5.97\times 10^{24} \text{kg}$

Distance from Sun to Earth = $1.50\times 10^{11} \text{m}$

1 Earth year = 365 Earth days

1 Earth day = 24 hours

The answer is 0.

2 solutions

July Thomas
Apr 20, 2016

Relevant wiki: Work

The definition of work is

$W = \vec{F}\bullet\vec{d} = Fd\cos\theta.$

The force of gravity points toward the center of the circular orbit. The displacement is always tangential to the orbit. Thus the angle between the two is $\theta = 90^{\circ}.$

$W = Fd\cos\theta = Fd\cos90 = Fd(0) = 0 \text{ J}$

Nikhesh Kumar
Aug 6, 2016

Work done by the sun is gravitational pull towards its centre of mass and it is actually a centripetal force. So the work done by the centripetal force is zero 0.

Work done by the Sun on the Earth

The answer is 0.

2 solutions

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