Wolfram Cloud Document

mUmaximum/.Solve[Sqrt[ c^5/((4Pi)^2*GblackbodyEmissivityBoltzmannConstant* CBRTemp^4)]==(2GmUmaximum)/c^2+(4GπmUmaximum)/c^2-( 4GπCos[(c^3t)/(GmUmaximum)]mUmaximum)/c^2/.t0, mUmaximum]/.{t0, BoltzmannConstantQuantity[1,"StefanBoltzmannConstant"], blackbodyEmissivity Quantity[1,"Joules"/("Meters"*"Meters"*"Seconds")], GQuantity[1,"GravitationalConstant"], cQuantity[1,"SpeedOfLight"],CBRTempQuantity[2.73,"Kelvins"]}

Out[]=



0.00533869

m

s

9/2

c

/(

2

K

3/2

G

J

σ

)



In[]:=

QuantityUnit[First[%]]UnitDimensions[%]DimensionalCombinations[{QuantityVariable["mUmx",%]},QuantityVariable["mss","Mass"],IncludeQuantities"PhysicalConstants",GeneratedParametersNone]First[Rest[%]]

Out[]=

Meters

Seconds

9/2

SpeedOfLight



3/2

GravitationalConstant

Joules

2

Kelvins

StefanBoltzmannConstant



Out[]=

MassUnit,

1

2

,TimeUnit,

3

2



Out[]=



1

9/14

h

/

3/7

G

1/7

QuantityVariable[mUmx,%]

,

1

9/4

c

/

3/4

G



QuantityVariable[mUmx,%]

,

1

3/2

h

/

3

c

QuantityVariable[mUmx,%]

,

1

/(

9/8

ε

0

3/4

G

9/8

μ

0

)



QuantityVariable[mUmx,%]

,

1

3/2

ε

0

3/2

μ

0

3/2

h

QuantityVariable[mUmx,%]

,

1

5/14

h

c

/

4/7

G



1/7

QuantityVariable[mUmx,%]

,

1

5/8

ε

0

5/8

μ

0

h

/

4

G

QuantityVariable[mUmx,%]

,

1

c

/(

5/8

ε

0

3/4

G

5/8

μ

0

)



QuantityVariable[mUmx,%]

,

1

2

ε

0

2

μ

0

3/2

h

c

QuantityVariable[mUmx,%]



$RecursionLimit

:Recursion depth of 1024 exceeded during evaluation of (!FreeQ[#1,Entity[PhysicalQuantity,_]]&)[mUmx].

$RecursionLimit

:Recursion depth of 1024 exceeded during evaluation of (!FreeQ[#1,Entity[PhysicalQuantity,_]]&)[%].

$RecursionLimit

:Recursion depth of 1024 exceeded during evaluation of QuantityUnits`Private`quantityUpValueFunctionQ[Times].

General

:Further output of $RecursionLimit::reclim2 will be suppressed during this calculation.

$RecursionLimit

:Recursion depth of 1024 exceeded during evaluation of Message[Message::msgl,Hold[{$RecursionLimit::reclim2,$RecursionLimit::reclim2,$RecursionLimit::reclim2,General::stop}]].

$RecursionLimit

:Recursion depth of 1024 exceeded during evaluation of {$RecursionLimit::reclim2}.

$RecursionLimit

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