h2eddsf3

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I am relatively new to Maple and I'm just getting used to working with units.  Please explain to me why the final calculation does not eliminate m^3 in both the numerator and denominator. Thanks for your help!

 

Problem

 

What would be the mass of a Dyson Shell set at Venus' orbit from the sun?

 

The shell is 150 ft thick and each 1m^2 section is 200 kg.

 

The entire Earth's mass is 5.97×10^24 kg

 

The entire mass of the solar system minus the sun is 2.6667×10^27 kg

``NULLNULL

Assumptions

 

Gravitational pull from the sun is uniform through the depth of the shell.

 

Venus' average orbital distance from the sun is 67,237,910 miles we will use that as.

Pi

Pi

(1)

"(->)"

3.1415926535897932385

(2)

 
Dyson[Inside] := 355016117130*Unit('ft')``

NULLDyson[Outside] := 355016117280*Unit('ft')

355016117280*Units:-Unit(ft)

(3)

NULLNULL``

Vol[Dyson] := (4/3)*Pi*Dyson[Outside]^3-(4/3)*Pi*Dyson[Inside]^3 = 75621866085188578208340000*Pi*Units:-Unit(ft^3)"(->)"0.23757309894397957472e27*Units:-Unit(ft^3)

   

Total_Weight := 200*Unit('kg')*Vol[Dyson]/m^3

(6691789940422039289112993734304/15625)*Pi*Units:-Unit(kg*m^3)/m^3

(4)

"(=)"

(6691789940422039289112993734304/15625)*Pi*Units:-Unit(kg*m^3)/m^3

(5)

"(->)"

0.13454641994365413638e28*Units:-Unit(kg*m^3)/m^3

(6)

Download Q_for_Dyson_Shell_Weight.mw

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