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Created December 21, 2022 17:13
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### A Pluto.jl notebook ###
# v0.19.9
using Markdown
using InteractiveUtils
# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
quote
local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
local el = $(esc(element))
global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
el
end
end
# ╔═╡ a0c338ce-5686-4844-acc4-d678eb9c57e6
using PlutoUI, Dates, TimeZones, AstroTime, Printf, LinearAlgebra
# ╔═╡ bbd0bfe0-75af-11ed-16c0-2ff9e2155437
md"
# The Subsolar Point
"
# ╔═╡ 5de17c26-afdc-442c-be0f-8f6810175a37
md"
The subsolar point is the point on the Earth where the Sun is directly overhead. Due to the rotation of the Earth and the inclination of the Earth's axis of rotation, the subsolar point moves continuously between the Tropics of Cancer and Capricorn.
Using your current location (latitude and longitude) and the date and time of day, the location of the subsolar point can be calculated, as well as the direction vector from your position to the Sun.
The results also give the azimuth and elevation angles to the Sun, and times of sunrise and sunset.
---
Load required modules:
"
# ╔═╡ a3b0dc0b-effa-4a60-aa9e-cb0e2f5210d0
md"
Some useful functions. Click the eye on to the left of each to view.
"
# ╔═╡ acd2cff0-a774-48c8-980b-40e66a119ef8
function decHours(T::Time)
Hrs = Dates.hour(T)
Mins = Dates.minute(T)
Secs = Dates.second(T)
mSecs = Dates.millisecond(T)
dT = Hrs + Mins/60.0 + (Secs + mSecs/1000)/3600.0
return dT
end
# ╔═╡ 7221d432-9741-47e2-b3bb-401f4f6cbad5
function yearFrac(DT::DateTime)
day_of_year = Dates.dayofyear(DT)
hour_frac = decHours(Time(DT)) / 24
YF = day_of_year + hour_frac
return YF
end
# ╔═╡ 1d4a15f3-6ca1-4129-b748-c2d683b45730
function RA2HMS(α)
# Right ascension is measured in hours, minutes, seconds from where the Sun crosses the equator at the Spring equinox. Since the Earth revolves 360 degrees in 24 hours, 360 deg / 24 hr = 15 deg/hr. Divide α by 15 to get time.
α_time = α/15
# Hours, minutes and seconds
Hrs = floor(α_time)
Mins = floor(60(α_time - Hrs))
Secs = 3600(α_time - Hrs - Mins/60)
# Right ascension in HH:MM:SS.sss
RA = @printf("%02d:%02d:%0.2f", Hrs, Mins, Secs)
return RA
end
# ╔═╡ 15d05071-772b-4c1d-8c7b-845cbb2dfa45
md"
Enter a latitude $(\phi_0)$ and longitude $(\lambda_0)$ position. Use [Google Earth](https://earth.google.com/web/) or [iTouchMap](https://itouchmap.com/?r=latlong). In Google Earth the decimal value of lat/lon can be copied from the address bar at the top.
Latitude (degrees):
"
# ╔═╡ 028a8e52-8452-46af-9166-bb9585a86012
@bind ϕ₀ NumberField(-90:0.00000001:90, default=35.92958111)
# ╔═╡ c8214d53-09ce-4e55-b2bb-883c5dfbf152
md"
Longitude (degrees):
"
# ╔═╡ 1c9a7012-09bb-4420-9b6d-5170429d3e6b
@bind λ₀ NumberField(-180:0.00000001:180, default=-79.08099136)
# ╔═╡ cc319226-dbc7-435f-9a49-4c89fa6f07aa
md"
Enter a date and time as [Coordinated Universal Time](https://www.utctime.net/) UTC (not local).
Date (yyyy-mm-dd):
"
# ╔═╡ b9491001-4e75-465d-b92e-cf11ed354a55
md"
Time (HH:MM:SS.sss):
"
# ╔═╡ ec2bf610-5a96-4579-aa60-35c9674301c1
md"
Click the Update button to reload date/time
"
# ╔═╡ f7b1c873-c079-4be7-bbbe-6bed5dbd089d
@bind update Button("Update date/time")
# ╔═╡ 7d68ef66-a0a7-40eb-9ac4-527776a4e5b9
begin
dt_utc = let
# Update date and time if button (below) is clicked
# Ref: https://github.com/JuliaPluto/PlutoUI.jl/issues/10
update
# Get current UTC date/time. Save as default values for inputs below.
dt_utc = DateTime(now(tz"UTC"))
end;
# Convert to string format
dateStr = Dates.format(dt_utc,"yyyy-mm-dd")
timeStr = Dates.format(dt_utc, "HH:MM:SS.sss")
end;
# ╔═╡ 80715f5f-2b7a-4325-abbd-84bc91e98e03
@bind LL_date TextField(default = dateStr)
# ╔═╡ 294aada9-4ac2-4098-94f9-e387da36c6fa
@bind LL_time TextField(default = timeStr)
# ╔═╡ e144c052-8c7e-4eee-b337-8d5d2f8946cf
begin
# Convert date and time to DateTime object
dtStr = LL_date * "T" * LL_time
dtObj = DateTime(dtStr)
end
# ╔═╡ 61991c16-13b5-43b2-acc8-9fe481d6f3be
md"
Number of days since January 1st, 2000 12:00 PM (incl. fractional days)
"
# ╔═╡ accb96ae-cf1b-49e7-81e8-1034dced5674
begin
nd = j2000(TAIEpoch(dtObj))
n = value(nd);
@printf("Number of days since J2000 = %8.3f days",n)
end;
# ╔═╡ 882befa1-73f8-4ab3-bce7-a7a3065d5c32
md"
Intermediate results (all in degrees)
"
# ╔═╡ 737de734-edea-4ed1-b930-8e6ac09bcf35
begin
L = mod(280.460 + 0.9856474n, 360)
g = mod(357.528 + 0.9856003n, 360)
λ = L + 1.915sind(g) + 0.02sind(2g)
ϵ = 23.440 - 0.0000004n
α = mod(atand(cosd(ϵ) * sind(λ), cosd(λ)),360)
δ = ϕₛ = asind(sind(ϵ) * sind(λ))
@printf("Solar longitude: L = %5.3f\n", L)
@printf("Mean anomaly: g = %5.3f\n", g)
@printf("Ecliptic longitude: λ = %5.3f\n", λ)
@printf("Obliquity of ecliptic: ϵ = %5.3f\n", ϵ)
@printf("Right ascension: α = %5.3f\n", α)
@printf("Declination: δ = %5.3f\n", δ)
end;
# ╔═╡ 1c37a6f3-d80f-45ca-85f5-827ca7d445c0
md"
Right ascension in HH:MM:SS.sss format
"
# ╔═╡ d2f87be5-41e8-40af-8fe0-79562f05d44b
RA2HMS(α)
# ╔═╡ da43ac9f-75c2-48d8-bb23-5f3e9a34b534
md"
The distance between Earth and Sun (measured in Atronomical Units (AU))
"
# ╔═╡ cceebc70-f65b-48f8-8e38-cac034191d54
RES = 1.00014 - 0.01671cos(g) - 0.00014cos(2g)
# ╔═╡ aabc104d-fb46-42c6-b973-f0f647a80f2c
md"
The Equation of Time
"
# ╔═╡ 869c601b-e8f6-44f2-8c4a-d5c7c40fec06
EoT = mod((L-α)+180, 360)-180
# ╔═╡ 9791dfd9-d11e-464c-b8e3-a86aff689fa9
md"
Time in decimal hours
"
# ╔═╡ d8e5519d-81e7-4e57-9d79-e50a5ef89da1
decHours(Time(LL_time))
# ╔═╡ c1e73d3b-5b9d-4cb2-a4df-e7fc9b62ef02
md"
The subsolar longitude
"
# ╔═╡ f99358a9-d28e-4775-ad2a-18d9df8eb12e
λₛ = -15(decHours(Time(LL_time)) - 12 + EoT/60)
# ╔═╡ f183d657-968f-4e8a-94e8-b75020d95102
md"
Solar pointing vector $S$.
"
# ╔═╡ d9b5741a-d3fe-45ae-9bc5-d5a6cf15e6ad
begin
S = [
cosd(ϕₛ)cosd(λₛ)
cosd(ϕₛ)sind(λₛ)
sind(ϕ₀)
]
S = S/norm(S)
end
# ╔═╡ 6e2056ee-9329-48c6-8afb-d4f39785f791
md"
Local upward vector $V$.
"
# ╔═╡ f4c0162f-1450-43d7-a138-83ee7e95c0e9
begin
V = [
cosd(ϕ₀)cosd(λ₀)
cosd(ϕ₀)sind(λ₀)
sind(ϕ₀)
]
V = V/norm(V)
end
# ╔═╡ 366cbd47-0451-4d7c-9e94-88ac0075e5e7
md"
Observer to Sun pointing vector (your position towards the Sun).
"
# ╔═╡ 4427bf63-37b7-4067-b631-7f0ea03e563d
begin
SV = [
cosd(ϕₛ)sind(λₛ - λ₀)
cosd(ϕ₀)sind(ϕₛ) - sind(ϕ₀)cosd(ϕₛ)cosd(λₛ - λ₀)
sind(ϕ₀)sind(ϕₛ) + cosd(ϕ₀)cosd(ϕₛ)cosd(λₛ - λ₀)
]
SV = SV/norm(SV)
end
# ╔═╡ aacbff70-c4cd-4c4d-98d7-32d46cccaa14
md"
Solar azimuth angle (North-clockwise)
"
# ╔═╡ deb526d8-8a8e-40d9-917c-6c7742ef8c73
Az = mod(atand(SV[1],SV[2]), 360)
# ╔═╡ 85862f45-ae8f-40e2-a985-e52f337ad75a
md"
Solar zenith and elevation angles
"
# ╔═╡ 7ac2fe8f-7db0-443d-8599-1a1c19c6cbad
Z = acosd(SV[3])
# ╔═╡ 5ec58de7-b05a-41d6-96c2-2947c4ac7a79
El = 90 - Z
# ╔═╡ 1661fcbd-24b6-4933-983f-7f69d6370145
md"
To be at the \"first day of summer\" you need to be at the subsolar point (ϕₛ, λₛ):
"
# ╔═╡ 1ce22d33-2350-4c5d-8acb-f1545c0ccca2
ϕₛ, λₛ
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
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PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
TimeZones = "f269a46b-ccf7-5d73-abea-4c690281aa53"
[compat]
AstroTime = "~0.7.0"
PlutoUI = "~0.7.49"
TimeZones = "~1.9.1"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
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[[deps.OptionalData]]
git-tree-sha1 = "d047cc114023e12292533bb822b45c23cb51d310"
uuid = "fbd9d27c-2d1c-5c1c-99f2-7497d746985d"
version = "1.0.0"
[[deps.OrderedCollections]]
git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.4.1"
[[deps.Parsers]]
deps = ["Dates", "SnoopPrecompile"]
git-tree-sha1 = "b64719e8b4504983c7fca6cc9db3ebc8acc2a4d6"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.5.1"
[[deps.Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
version = "1.8.0"
[[deps.PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "ColorTypes", "Dates", "FixedPointNumbers", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "MIMEs", "Markdown", "Random", "Reexport", "URIs", "UUIDs"]
git-tree-sha1 = "eadad7b14cf046de6eb41f13c9275e5aa2711ab6"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.49"
[[deps.Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
[[deps.REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
[[deps.Random]]
deps = ["SHA", "Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
[[deps.RecipesBase]]
deps = ["SnoopPrecompile"]
git-tree-sha1 = "18c35ed630d7229c5584b945641a73ca83fb5213"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.3.2"
[[deps.Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"
[[deps.RemoteFiles]]
deps = ["Dates", "FileIO", "HTTP"]
git-tree-sha1 = "54527375d877a64c55190fb762d584f927d6d7c3"
uuid = "cbe49d4c-5af1-5b60-bb70-0a60aa018e1b"
version = "0.4.2"
[[deps.Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.3.0"
[[deps.SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
version = "0.7.0"
[[deps.Scratch]]
deps = ["Dates"]
git-tree-sha1 = "f94f779c94e58bf9ea243e77a37e16d9de9126bd"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.1.1"
[[deps.Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
[[deps.SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
[[deps.SimpleTraits]]
deps = ["InteractiveUtils", "MacroTools"]
git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
version = "0.9.4"
[[deps.SnoopPrecompile]]
git-tree-sha1 = "f604441450a3c0569830946e5b33b78c928e1a85"
uuid = "66db9d55-30c0-4569-8b51-7e840670fc0c"
version = "1.0.1"
[[deps.Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
[[deps.SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
[[deps.StaticArrays]]
deps = ["LinearAlgebra", "Random", "StaticArraysCore", "Statistics"]
git-tree-sha1 = "ffc098086f35909741f71ce21d03dadf0d2bfa76"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.5.11"
[[deps.StaticArraysCore]]
git-tree-sha1 = "6b7ba252635a5eff6a0b0664a41ee140a1c9e72a"
uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
version = "1.4.0"
[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.0"
[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.0"
[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
[[deps.TimeZones]]
deps = ["Dates", "Downloads", "InlineStrings", "LazyArtifacts", "Mocking", "Printf", "RecipesBase", "Scratch", "Unicode"]
git-tree-sha1 = "a92ec4466fc6e3dd704e2668b5e7f24add36d242"
uuid = "f269a46b-ccf7-5d73-abea-4c690281aa53"
version = "1.9.1"
[[deps.Tricks]]
git-tree-sha1 = "6bac775f2d42a611cdfcd1fb217ee719630c4175"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.6"
[[deps.URIs]]
git-tree-sha1 = "ac00576f90d8a259f2c9d823e91d1de3fd44d348"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.4.1"
[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.12+3"
[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.1.1+0"
[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.48.0+0"
[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"
"""
# ╔═╡ Cell order:
# ╟─bbd0bfe0-75af-11ed-16c0-2ff9e2155437
# ╟─5de17c26-afdc-442c-be0f-8f6810175a37
# ╠═a0c338ce-5686-4844-acc4-d678eb9c57e6
# ╟─a3b0dc0b-effa-4a60-aa9e-cb0e2f5210d0
# ╟─acd2cff0-a774-48c8-980b-40e66a119ef8
# ╟─7221d432-9741-47e2-b3bb-401f4f6cbad5
# ╟─1d4a15f3-6ca1-4129-b748-c2d683b45730
# ╟─7d68ef66-a0a7-40eb-9ac4-527776a4e5b9
# ╟─15d05071-772b-4c1d-8c7b-845cbb2dfa45
# ╟─028a8e52-8452-46af-9166-bb9585a86012
# ╟─c8214d53-09ce-4e55-b2bb-883c5dfbf152
# ╟─1c9a7012-09bb-4420-9b6d-5170429d3e6b
# ╟─cc319226-dbc7-435f-9a49-4c89fa6f07aa
# ╟─80715f5f-2b7a-4325-abbd-84bc91e98e03
# ╟─b9491001-4e75-465d-b92e-cf11ed354a55
# ╟─294aada9-4ac2-4098-94f9-e387da36c6fa
# ╟─ec2bf610-5a96-4579-aa60-35c9674301c1
# ╟─f7b1c873-c079-4be7-bbbe-6bed5dbd089d
# ╟─e144c052-8c7e-4eee-b337-8d5d2f8946cf
# ╟─61991c16-13b5-43b2-acc8-9fe481d6f3be
# ╟─accb96ae-cf1b-49e7-81e8-1034dced5674
# ╟─882befa1-73f8-4ab3-bce7-a7a3065d5c32
# ╟─737de734-edea-4ed1-b930-8e6ac09bcf35
# ╟─1c37a6f3-d80f-45ca-85f5-827ca7d445c0
# ╟─d2f87be5-41e8-40af-8fe0-79562f05d44b
# ╟─da43ac9f-75c2-48d8-bb23-5f3e9a34b534
# ╟─cceebc70-f65b-48f8-8e38-cac034191d54
# ╟─aabc104d-fb46-42c6-b973-f0f647a80f2c
# ╟─869c601b-e8f6-44f2-8c4a-d5c7c40fec06
# ╟─9791dfd9-d11e-464c-b8e3-a86aff689fa9
# ╟─d8e5519d-81e7-4e57-9d79-e50a5ef89da1
# ╟─c1e73d3b-5b9d-4cb2-a4df-e7fc9b62ef02
# ╟─f99358a9-d28e-4775-ad2a-18d9df8eb12e
# ╟─f183d657-968f-4e8a-94e8-b75020d95102
# ╟─d9b5741a-d3fe-45ae-9bc5-d5a6cf15e6ad
# ╟─6e2056ee-9329-48c6-8afb-d4f39785f791
# ╟─f4c0162f-1450-43d7-a138-83ee7e95c0e9
# ╟─366cbd47-0451-4d7c-9e94-88ac0075e5e7
# ╟─4427bf63-37b7-4067-b631-7f0ea03e563d
# ╟─aacbff70-c4cd-4c4d-98d7-32d46cccaa14
# ╟─deb526d8-8a8e-40d9-917c-6c7742ef8c73
# ╟─85862f45-ae8f-40e2-a985-e52f337ad75a
# ╠═7ac2fe8f-7db0-443d-8599-1a1c19c6cbad
# ╟─5ec58de7-b05a-41d6-96c2-2947c4ac7a79
# ╟─1661fcbd-24b6-4933-983f-7f69d6370145
# ╟─1ce22d33-2350-4c5d-8acb-f1545c0ccca2
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
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