Follow the Sun as It Moves across the Sky 

Determine your final location if you walk toward the Sun from sunrise to sunset at a constant speed.

In[1]:=

X location = Entity["Building", "WhiteHouse"][ EntityProperty["Building", "Position"]]; speed = \!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{WolframAlphaClient`Private`query$$ = "4 mph", WolframAlphaClient`Private`boxes$$ = TemplateBox[{"4"}, "QuantityUnit", DisplayFunction -> (TooltipBox[ StyleBox[ RowBox[{#, " ", StyleBox[ RowBox[{" ", RowBox[{"\"mi\"", " ", "\"/\"", " ", "\"h\""}]}], "QuantityUnitTraditionalInput"]}], ShowStringCharacters -> False], "Unit: miles per hour"]& ), InterpretationFunction -> (RowBox[{"Quantity", "[", RowBox[{#, ",", FractionBox["\"Miles\"", "\"Hours\""]}], "]"}]& ), SyntaxForm -> Mod], WolframAlphaClient`Private`allassumptions$$ = {}, WolframAlphaClient`Private`assumptions$$ = {}, WolframAlphaClient`Private`open$$ = {1}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 1, Dynamic[WolframAlphaClient`Private`query$$], Dynamic[WolframAlphaClient`Private`boxes$$], Dynamic[WolframAlphaClient`Private`allassumptions$$], Dynamic[WolframAlphaClient`Private`assumptions$$], Dynamic[WolframAlphaClient`Private`open$$]], StandardForm], ImageSizeCache->{57., {7., 16.}}, TrackedSymbols:>{ WolframAlphaClient`Private`query$$, WolframAlphaClient`Private`boxes$$, WolframAlphaClient`Private`allassumptions$$, WolframAlphaClient`Private`assumptions$$, WolframAlphaClient`Private`open$$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{WolframAlphaClient`Private`open$$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\); deltaT = \!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{WolframAlphaClient`Private`query$$ = "10 min", WolframAlphaClient`Private`boxes$$ = TemplateBox[{"10"}, "QuantityUnit", DisplayFunction -> (TooltipBox[ StyleBox[ RowBox[{#, " ", StyleBox[ RowBox[{" ", "\"min\""}], "QuantityUnitTraditionalInput"]}], ShowStringCharacters -> False], "Unit: minutes"]& ), InterpretationFunction -> (RowBox[{"Quantity", "[", RowBox[{#, ",", "\"Minutes\""}], "]"}]& ), SyntaxForm -> Mod], WolframAlphaClient`Private`allassumptions$$ = {{ "type" -> "Clash", "word" -> "min", "template" -> "Assuming \"${word}\" is ${desc1}. Use as \ ${desc2} instead", "count" -> "2", "Values" -> {{ "name" -> "Unit", "desc" -> "a unit", "input" -> "*C.min-_*Unit-"}, { "name" -> "OptimizationWord", "desc" -> " referring to optimization", "input" -> "*C.min-_*OptimizationWord-"}}}, { "type" -> "Unit", "word" -> "min", "template" -> "Assuming ${desc1} for \"${word}\". Use \ ${desc2} instead", "count" -> "3", "Values" -> {{ "name" -> "Minutes", "desc" -> "minutes of time", "input" -> "UnitClash_*min.*Minutes--"}, { "name" -> "MinimsUS", "desc" -> "US minims of volume", "input" -> "UnitClash_*min.*MinimsUS--"}, { "name" -> "ArcMinutes", "desc" -> "minutes of arc", "input" -> "UnitClash_*min.*ArcMinutes--"}}}}, WolframAlphaClient`Private`assumptions$$ = {}, WolframAlphaClient`Private`open$$ = {1}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 1, Dynamic[WolframAlphaClient`Private`query$$], Dynamic[WolframAlphaClient`Private`boxes$$], Dynamic[WolframAlphaClient`Private`allassumptions$$], Dynamic[WolframAlphaClient`Private`assumptions$$], Dynamic[WolframAlphaClient`Private`open$$]], StandardForm], ImageSizeCache->{60., {7., 16.}}, TrackedSymbols:>{ WolframAlphaClient`Private`query$$, WolframAlphaClient`Private`boxes$$, WolframAlphaClient`Private`allassumptions$$, WolframAlphaClient`Private`assumptions$$, WolframAlphaClient`Private`open$$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{WolframAlphaClient`Private`open$$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\); start = Sunrise[location, \!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{WolframAlphaClient`Private`query$$ = "July 4", WolframAlphaClient`Private`boxes$$ = RowBox[{"DateObject", "[", RowBox[{"{", RowBox[{"2014", ",", " ", "7", ",", " ", "4"}], "}"}], "]"}], WolframAlphaClient`Private`allassumptions$$ = {}, WolframAlphaClient`Private`assumptions$$ = {}, WolframAlphaClient`Private`open$$ = {1}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 1, Dynamic[WolframAlphaClient`Private`query$$], Dynamic[WolframAlphaClient`Private`boxes$$], Dynamic[WolframAlphaClient`Private`allassumptions$$], Dynamic[WolframAlphaClient`Private`assumptions$$], Dynamic[WolframAlphaClient`Private`open$$]], StandardForm], ImageSizeCache->{55., {7., 16.}}, TrackedSymbols:>{ WolframAlphaClient`Private`query$$, WolframAlphaClient`Private`boxes$$, WolframAlphaClient`Private`allassumptions$$, WolframAlphaClient`Private`assumptions$$, WolframAlphaClient`Private`open$$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{WolframAlphaClient`Private`open$$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\)]; end = Sunset[location, \!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{WolframAlphaClient`Private`query$$ = "July 4", WolframAlphaClient`Private`boxes$$ = RowBox[{"DateObject", "[", RowBox[{"{", RowBox[{"2014", ",", " ", "7", ",", " ", "4"}], "}"}], "]"}], WolframAlphaClient`Private`allassumptions$$ = {}, WolframAlphaClient`Private`assumptions$$ = {}, WolframAlphaClient`Private`open$$ = {1}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 1, Dynamic[WolframAlphaClient`Private`query$$], Dynamic[WolframAlphaClient`Private`boxes$$], Dynamic[WolframAlphaClient`Private`allassumptions$$], Dynamic[WolframAlphaClient`Private`assumptions$$], Dynamic[WolframAlphaClient`Private`open$$]], StandardForm], ImageSizeCache->{55., {7., 16.}}, TrackedSymbols:>{ WolframAlphaClient`Private`query$$, WolframAlphaClient`Private`boxes$$, WolframAlphaClient`Private`allassumptions$$, WolframAlphaClient`Private`assumptions$$, WolframAlphaClient`Private`open$$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{WolframAlphaClient`Private`open$$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\)];

Iterate the bearing in 10-minute increments to obtain a new course and destination.

In[2]:=

X locs = Table[ location = GeoDestination[ location, {speed deltaT, SunPosition[location, DateObject[time]][[1]]}], {time, AbsoluteTime[start], AbsoluteTime[end], QuantityMagnitude[ UnitConvert[Quantity[10, "Minutes"], "Seconds"]]}];

Visualize the resulting path.

In[3]:=

X GeoGraphics[{RGBColor[.49, 0, 0], Thickness[.007], Line[locs]}, GeoRange -> {{38.63, 39.1}, {-77.1, -76.5}}]

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