2 added 254 characters in body
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f[x_?NumberQ] := MoonPosition[DateObject[{2016, 9, 28, x}]][[2, 1]]

FindRoot[Evaluate@f[x]FindRoot[f[x], {x, 12}]

{x -> 17.5595}

ListPlot[Table[{x, f[x]}, {x, 1, 24, 0.5}], Frame -> True, FrameLabel -> {"x", "f(x)"}]

enter image description here

So another root is at about 4:

FindRoot[f[x], {x, 4}]

{x -> 3.7208}

f[x_?NumberQ] := MoonPosition[DateObject[{2016, 9, 28, x}]][[2, 1]]

FindRoot[Evaluate@f[x], {x, 12}]

{x -> 17.5595}

f[x_?NumberQ] := MoonPosition[DateObject[{2016, 9, 28, x}]][[2, 1]]

FindRoot[f[x], {x, 12}]

{x -> 17.5595}

ListPlot[Table[{x, f[x]}, {x, 1, 24, 0.5}], Frame -> True, FrameLabel -> {"x", "f(x)"}]

enter image description here

So another root is at about 4:

FindRoot[f[x], {x, 4}]

{x -> 3.7208}

1
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f[x_?NumberQ] := MoonPosition[DateObject[{2016, 9, 28, x}]][[2, 1]]

FindRoot[Evaluate@f[x], {x, 12}]

{x -> 17.5595}