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How much energy would be required to move the earth into a circular orbit with a radius 1.0km larger than its current radius?

Short Answer

Expert verified

Total of1.89×1025Jenergy would be required to move the earth into a circular orbit with a radius1.0km.

Step by step solution

01

Given Information

New radius of the circular orbit is 1.0kmlarger than the current radius.

02

Formula used

Excess energy ∆E=GMm2R-GMm2R+r

Here, gravitational constant G=6.67×10-11N·m2/kg2.

Mass of the sun, localid="1648185717314" M=1.989×1030kg.

Mass of the earth, m=5.97×1024kg.

Initial radius of earth's orbit, localid="1648185813557" R=1.5×1011m.

New radius of earth's orbit,R+r=1.5×1011+103m.

03

:  Calculation

Substitute the values and obtain∆E.

∆E=GMm2R-GMm2R+r∆E=GMm21R-1R+r∆E=6.67×10-11N·m2/kg2×1.989×1030kg×5.97×1024kg211.5×1011m-11.5×1011m+103m∆E=39.6×1043×4.78×10-20J∆E=1.89×1025J
04

Final Answer

Total of1.89×1025Jenergy would be required to move the earth into a circular orbit with a radius1.0km .

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