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1642 lines
60 KiB
HTML
1642 lines
60 KiB
HTML
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||
.base-grid,
|
||
distill-header,
|
||
d-title,
|
||
d-abstract,
|
||
d-article,
|
||
d-appendix,
|
||
distill-appendix,
|
||
d-byline,
|
||
d-footnote-list,
|
||
d-citation-list,
|
||
distill-footer {
|
||
grid-template-columns: [screen-start] 1fr [page-start kicker-start] 80px [middle-start] 50px [text-start kicker-end] 65px 65px 65px 65px 65px 65px 65px 65px [text-end gutter-start] 65px [middle-end] 65px [page-end gutter-end] 1fr [screen-end];
|
||
grid-column-gap: 16px;
|
||
}
|
||
|
||
.grid {
|
||
grid-column-gap: 16px;
|
||
}
|
||
|
||
d-article {
|
||
font-size: 1.06rem;
|
||
line-height: 1.7em;
|
||
}
|
||
figure .caption, .figure .caption, figure figcaption {
|
||
font-size: 13px;
|
||
}
|
||
}
|
||
|
||
@media(min-width: 1180px) {
|
||
.base-grid,
|
||
distill-header,
|
||
d-title,
|
||
d-abstract,
|
||
d-article,
|
||
d-appendix,
|
||
distill-appendix,
|
||
d-byline,
|
||
d-footnote-list,
|
||
d-citation-list,
|
||
distill-footer {
|
||
grid-template-columns: [screen-start] 1fr [page-start kicker-start] 60px [middle-start] 60px [text-start kicker-end] 60px 60px 60px 60px 60px 60px 60px 60px [text-end gutter-start] 60px [middle-end] 60px [page-end gutter-end] 1fr [screen-end];
|
||
grid-column-gap: 32px;
|
||
}
|
||
|
||
.grid {
|
||
grid-column-gap: 32px;
|
||
}
|
||
}
|
||
|
||
|
||
/* Get the citation styles for the appendix (not auto-injected on render since
|
||
we do our own rendering of the citation appendix) */
|
||
|
||
d-appendix .citation-appendix,
|
||
.d-appendix .citation-appendix {
|
||
font-size: 11px;
|
||
line-height: 15px;
|
||
border-left: 1px solid rgba(0, 0, 0, 0.1);
|
||
padding-left: 18px;
|
||
border: 1px solid rgba(0,0,0,0.1);
|
||
background: rgba(0, 0, 0, 0.02);
|
||
padding: 10px 18px;
|
||
border-radius: 3px;
|
||
color: rgba(150, 150, 150, 1);
|
||
overflow: hidden;
|
||
margin-top: -12px;
|
||
white-space: pre-wrap;
|
||
word-wrap: break-word;
|
||
}
|
||
|
||
/* Include appendix styles here so they can be overridden */
|
||
|
||
d-appendix {
|
||
contain: layout style;
|
||
font-size: 0.8em;
|
||
line-height: 1.7em;
|
||
margin-top: 60px;
|
||
margin-bottom: 0;
|
||
border-top: 1px solid rgba(0, 0, 0, 0.1);
|
||
color: rgba(0,0,0,0.5);
|
||
padding-top: 60px;
|
||
padding-bottom: 48px;
|
||
}
|
||
|
||
d-appendix h3 {
|
||
grid-column: page-start / text-start;
|
||
font-size: 15px;
|
||
font-weight: 500;
|
||
margin-top: 1em;
|
||
margin-bottom: 0;
|
||
color: rgba(0,0,0,0.65);
|
||
}
|
||
|
||
d-appendix h3 + * {
|
||
margin-top: 1em;
|
||
}
|
||
|
||
d-appendix ol {
|
||
padding: 0 0 0 15px;
|
||
}
|
||
|
||
@media (min-width: 768px) {
|
||
d-appendix ol {
|
||
padding: 0 0 0 30px;
|
||
margin-left: -30px;
|
||
}
|
||
}
|
||
|
||
d-appendix li {
|
||
margin-bottom: 1em;
|
||
}
|
||
|
||
d-appendix a {
|
||
color: rgba(0, 0, 0, 0.6);
|
||
}
|
||
|
||
d-appendix > * {
|
||
grid-column: text;
|
||
}
|
||
|
||
d-appendix > d-footnote-list,
|
||
d-appendix > d-citation-list,
|
||
d-appendix > distill-appendix {
|
||
grid-column: screen;
|
||
}
|
||
|
||
/* Include footnote styles here so they can be overridden */
|
||
|
||
d-footnote-list {
|
||
contain: layout style;
|
||
}
|
||
|
||
d-footnote-list > * {
|
||
grid-column: text;
|
||
}
|
||
|
||
d-footnote-list a.footnote-backlink {
|
||
color: rgba(0,0,0,0.3);
|
||
padding-left: 0.5em;
|
||
}
|
||
|
||
|
||
|
||
/* Anchor.js */
|
||
|
||
.anchorjs-link {
|
||
/*transition: all .25s linear; */
|
||
text-decoration: none;
|
||
border-bottom: none;
|
||
}
|
||
*:hover > .anchorjs-link {
|
||
margin-left: -1.125em !important;
|
||
text-decoration: none;
|
||
border-bottom: none;
|
||
}
|
||
|
||
/* Social footer */
|
||
|
||
.social_footer {
|
||
margin-top: 30px;
|
||
margin-bottom: 0;
|
||
color: rgba(0,0,0,0.67);
|
||
}
|
||
|
||
.disqus-comments {
|
||
margin-right: 30px;
|
||
}
|
||
|
||
.disqus-comment-count {
|
||
border-bottom: 1px solid rgba(0, 0, 0, 0.4);
|
||
cursor: pointer;
|
||
}
|
||
|
||
#disqus_thread {
|
||
margin-top: 30px;
|
||
}
|
||
|
||
.article-sharing a {
|
||
border-bottom: none;
|
||
margin-right: 8px;
|
||
}
|
||
|
||
.article-sharing a:hover {
|
||
border-bottom: none;
|
||
}
|
||
|
||
.sidebar-section.subscribe {
|
||
font-size: 12px;
|
||
line-height: 1.6em;
|
||
}
|
||
|
||
.subscribe p {
|
||
margin-bottom: 0.5em;
|
||
}
|
||
|
||
|
||
.article-footer .subscribe {
|
||
font-size: 15px;
|
||
margin-top: 45px;
|
||
}
|
||
|
||
|
||
.sidebar-section.custom {
|
||
font-size: 12px;
|
||
line-height: 1.6em;
|
||
}
|
||
|
||
.custom p {
|
||
margin-bottom: 0.5em;
|
||
}
|
||
|
||
/* Styles for listing layout (hide title) */
|
||
.layout-listing d-title, .layout-listing .d-title {
|
||
display: none;
|
||
}
|
||
|
||
/* Styles for posts lists (not auto-injected) */
|
||
|
||
|
||
.posts-with-sidebar {
|
||
padding-left: 45px;
|
||
padding-right: 45px;
|
||
}
|
||
|
||
.posts-list .description h2,
|
||
.posts-list .description p {
|
||
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen, Ubuntu, Cantarell, "Fira Sans", "Droid Sans", "Helvetica Neue", Arial, sans-serif;
|
||
}
|
||
|
||
.posts-list .description h2 {
|
||
font-weight: 700;
|
||
border-bottom: none;
|
||
padding-bottom: 0;
|
||
}
|
||
|
||
.posts-list h2.post-tag {
|
||
border-bottom: 1px solid rgba(0, 0, 0, 0.2);
|
||
padding-bottom: 12px;
|
||
}
|
||
.posts-list {
|
||
margin-top: 60px;
|
||
margin-bottom: 24px;
|
||
}
|
||
|
||
.posts-list .post-preview {
|
||
text-decoration: none;
|
||
overflow: hidden;
|
||
display: block;
|
||
border-bottom: 1px solid rgba(0, 0, 0, 0.1);
|
||
padding: 24px 0;
|
||
}
|
||
|
||
.post-preview-last {
|
||
border-bottom: none !important;
|
||
}
|
||
|
||
.posts-list .posts-list-caption {
|
||
grid-column: screen;
|
||
font-weight: 400;
|
||
}
|
||
|
||
.posts-list .post-preview h2 {
|
||
margin: 0 0 6px 0;
|
||
line-height: 1.2em;
|
||
font-style: normal;
|
||
font-size: 24px;
|
||
}
|
||
|
||
.posts-list .post-preview p {
|
||
margin: 0 0 12px 0;
|
||
line-height: 1.4em;
|
||
font-size: 16px;
|
||
}
|
||
|
||
.posts-list .post-preview .thumbnail {
|
||
box-sizing: border-box;
|
||
margin-bottom: 24px;
|
||
position: relative;
|
||
max-width: 500px;
|
||
}
|
||
.posts-list .post-preview img {
|
||
width: 100%;
|
||
display: block;
|
||
}
|
||
|
||
.posts-list .metadata {
|
||
font-size: 12px;
|
||
line-height: 1.4em;
|
||
margin-bottom: 18px;
|
||
}
|
||
|
||
.posts-list .metadata > * {
|
||
display: inline-block;
|
||
}
|
||
|
||
.posts-list .metadata .publishedDate {
|
||
margin-right: 2em;
|
||
}
|
||
|
||
.posts-list .metadata .dt-authors {
|
||
display: block;
|
||
margin-top: 0.3em;
|
||
margin-right: 2em;
|
||
}
|
||
|
||
.posts-list .dt-tags {
|
||
display: block;
|
||
line-height: 1em;
|
||
}
|
||
|
||
.posts-list .dt-tags .dt-tag {
|
||
display: inline-block;
|
||
color: rgba(0,0,0,0.6);
|
||
padding: 0.3em 0.4em;
|
||
margin-right: 0.2em;
|
||
margin-bottom: 0.4em;
|
||
font-size: 60%;
|
||
border: 1px solid rgba(0,0,0,0.2);
|
||
border-radius: 3px;
|
||
text-transform: uppercase;
|
||
font-weight: 500;
|
||
}
|
||
|
||
.posts-list img {
|
||
opacity: 1;
|
||
}
|
||
|
||
.posts-list img[data-src] {
|
||
opacity: 0;
|
||
}
|
||
|
||
.posts-more {
|
||
clear: both;
|
||
}
|
||
|
||
|
||
.posts-sidebar {
|
||
font-size: 16px;
|
||
}
|
||
|
||
.posts-sidebar h3 {
|
||
font-size: 16px;
|
||
margin-top: 0;
|
||
margin-bottom: 0.5em;
|
||
font-weight: 400;
|
||
text-transform: uppercase;
|
||
}
|
||
|
||
.sidebar-section {
|
||
margin-bottom: 30px;
|
||
}
|
||
|
||
.categories ul {
|
||
list-style-type: none;
|
||
margin: 0;
|
||
padding: 0;
|
||
}
|
||
|
||
.categories li {
|
||
color: rgba(0, 0, 0, 0.8);
|
||
margin-bottom: 0;
|
||
}
|
||
|
||
.categories li>a {
|
||
border-bottom: none;
|
||
}
|
||
|
||
.categories li>a:hover {
|
||
border-bottom: 1px solid rgba(0, 0, 0, 0.4);
|
||
}
|
||
|
||
.categories .active {
|
||
font-weight: 600;
|
||
}
|
||
|
||
.categories .category-count {
|
||
color: rgba(0, 0, 0, 0.4);
|
||
}
|
||
|
||
|
||
@media(min-width: 768px) {
|
||
.posts-list .post-preview h2 {
|
||
font-size: 26px;
|
||
}
|
||
.posts-list .post-preview .thumbnail {
|
||
float: right;
|
||
width: 30%;
|
||
margin-bottom: 0;
|
||
}
|
||
.posts-list .post-preview .description {
|
||
float: left;
|
||
width: 45%;
|
||
}
|
||
.posts-list .post-preview .metadata {
|
||
float: left;
|
||
width: 20%;
|
||
margin-top: 8px;
|
||
}
|
||
.posts-list .post-preview p {
|
||
margin: 0 0 12px 0;
|
||
line-height: 1.5em;
|
||
font-size: 16px;
|
||
}
|
||
.posts-with-sidebar .posts-list {
|
||
float: left;
|
||
width: 75%;
|
||
}
|
||
.posts-with-sidebar .posts-sidebar {
|
||
float: right;
|
||
width: 20%;
|
||
margin-top: 60px;
|
||
padding-top: 24px;
|
||
padding-bottom: 24px;
|
||
}
|
||
}
|
||
|
||
|
||
/* Improve display for browsers without grid (IE/Edge <= 15) */
|
||
|
||
.downlevel {
|
||
line-height: 1.6em;
|
||
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen, Ubuntu, Cantarell, "Fira Sans", "Droid Sans", "Helvetica Neue", Arial, sans-serif;
|
||
margin: 0;
|
||
}
|
||
|
||
.downlevel .d-title {
|
||
padding-top: 6rem;
|
||
padding-bottom: 1.5rem;
|
||
}
|
||
|
||
.downlevel .d-title h1 {
|
||
font-size: 50px;
|
||
font-weight: 700;
|
||
line-height: 1.1em;
|
||
margin: 0 0 0.5rem;
|
||
}
|
||
|
||
.downlevel .d-title p {
|
||
font-weight: 300;
|
||
font-size: 1.2rem;
|
||
line-height: 1.55em;
|
||
margin-top: 0;
|
||
}
|
||
|
||
.downlevel .d-byline {
|
||
padding-top: 0.8em;
|
||
padding-bottom: 0.8em;
|
||
font-size: 0.8rem;
|
||
line-height: 1.8em;
|
||
}
|
||
|
||
.downlevel .section-separator {
|
||
border: none;
|
||
border-top: 1px solid rgba(0, 0, 0, 0.1);
|
||
}
|
||
|
||
.downlevel .d-article {
|
||
font-size: 1.06rem;
|
||
line-height: 1.7em;
|
||
padding-top: 1rem;
|
||
padding-bottom: 2rem;
|
||
}
|
||
|
||
|
||
.downlevel .d-appendix {
|
||
padding-left: 0;
|
||
padding-right: 0;
|
||
max-width: none;
|
||
font-size: 0.8em;
|
||
line-height: 1.7em;
|
||
margin-bottom: 0;
|
||
color: rgba(0,0,0,0.5);
|
||
padding-top: 40px;
|
||
padding-bottom: 48px;
|
||
}
|
||
|
||
.downlevel .footnotes ol {
|
||
padding-left: 13px;
|
||
}
|
||
|
||
.downlevel .base-grid,
|
||
.downlevel .distill-header,
|
||
.downlevel .d-title,
|
||
.downlevel .d-abstract,
|
||
.downlevel .d-article,
|
||
.downlevel .d-appendix,
|
||
.downlevel .distill-appendix,
|
||
.downlevel .d-byline,
|
||
.downlevel .d-footnote-list,
|
||
.downlevel .d-citation-list,
|
||
.downlevel .distill-footer,
|
||
.downlevel .appendix-bottom,
|
||
.downlevel .posts-container {
|
||
padding-left: 40px;
|
||
padding-right: 40px;
|
||
}
|
||
|
||
@media(min-width: 768px) {
|
||
.downlevel .base-grid,
|
||
.downlevel .distill-header,
|
||
.downlevel .d-title,
|
||
.downlevel .d-abstract,
|
||
.downlevel .d-article,
|
||
.downlevel .d-appendix,
|
||
.downlevel .distill-appendix,
|
||
.downlevel .d-byline,
|
||
.downlevel .d-footnote-list,
|
||
.downlevel .d-citation-list,
|
||
.downlevel .distill-footer,
|
||
.downlevel .appendix-bottom,
|
||
.downlevel .posts-container {
|
||
padding-left: 150px;
|
||
padding-right: 150px;
|
||
max-width: 900px;
|
||
}
|
||
}
|
||
|
||
.downlevel pre code {
|
||
display: block;
|
||
border-left: 2px solid rgba(0, 0, 0, .1);
|
||
padding: 0 0 0 20px;
|
||
font-size: 14px;
|
||
}
|
||
|
||
.downlevel code, .downlevel pre {
|
||
color: black;
|
||
background: none;
|
||
font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;
|
||
text-align: left;
|
||
white-space: pre;
|
||
word-spacing: normal;
|
||
word-break: normal;
|
||
word-wrap: normal;
|
||
line-height: 1.5;
|
||
|
||
-moz-tab-size: 4;
|
||
-o-tab-size: 4;
|
||
tab-size: 4;
|
||
|
||
-webkit-hyphens: none;
|
||
-moz-hyphens: none;
|
||
-ms-hyphens: none;
|
||
hyphens: none;
|
||
}
|
||
|
||
.downlevel .posts-list .post-preview {
|
||
color: inherit;
|
||
}
|
||
|
||
|
||
|
||
</style>
|
||
|
||
<script type="application/javascript">
|
||
|
||
function is_downlevel_browser() {
|
||
if (bowser.isUnsupportedBrowser({ msie: "12", msedge: "16"},
|
||
window.navigator.userAgent)) {
|
||
return true;
|
||
} else {
|
||
return window.load_distill_framework === undefined;
|
||
}
|
||
}
|
||
|
||
// show body when load is complete
|
||
function on_load_complete() {
|
||
|
||
// add anchors
|
||
if (window.anchors) {
|
||
window.anchors.options.placement = 'left';
|
||
window.anchors.add('d-article > h2, d-article > h3, d-article > h4, d-article > h5');
|
||
}
|
||
|
||
|
||
// set body to visible
|
||
document.body.style.visibility = 'visible';
|
||
|
||
// force redraw for leaflet widgets
|
||
if (window.HTMLWidgets) {
|
||
var maps = window.HTMLWidgets.findAll(".leaflet");
|
||
$.each(maps, function(i, el) {
|
||
var map = this.getMap();
|
||
map.invalidateSize();
|
||
map.eachLayer(function(layer) {
|
||
if (layer instanceof L.TileLayer)
|
||
layer.redraw();
|
||
});
|
||
});
|
||
}
|
||
|
||
// trigger 'shown' so htmlwidgets resize
|
||
$('d-article').trigger('shown');
|
||
}
|
||
|
||
function init_distill() {
|
||
|
||
init_common();
|
||
|
||
// create front matter
|
||
var front_matter = $('<d-front-matter></d-front-matter>');
|
||
$('#distill-front-matter').wrap(front_matter);
|
||
|
||
// create d-title
|
||
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<h1>ISS Eclipse Determination</h1>
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<!--radix_placeholder_categories-->
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<div class="dt=tag">Julia</div>
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<p><p>Determining how much sunlight a body orbiting a planet is receiving.</p></p>
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Anson Biggs <a href="https://ansonbiggs.com" class="uri">https://ansonbiggs.com</a>
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<br/>05-01-2021
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<div class="d-article">
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<p>Determining the eclipses a satellite will encounter is a major driving factor when designing a mission in space. Thermal and power budgets have to be made with the fact that a satellite will periodically be in the complete darkness of space where it will receive no solar radiation to power the solar panels and keep the spacecraft from freezing.</p>
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<h2 id="what-is-an-eclipse">What is an Eclipse</h2>
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||
<p>The above image is a simple representation of what an eclipse is. First, you’ll notice the Umbra is complete darkness, then the Penumbra, which is a shadow of varying darkness, and then the rest of the orbit is in full sunlight. For this example, I will be using the ISS, which has a very low orbit, so the Penumbra isn’t much of a problem. However, you can tell by looking at the diagram that higher altitude orbits would spend more time in the Penumbra.</p>
|
||
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||
<img src="vectors_radiuss.svg" alt="Body Radius’s and Position Vectors" /><figcaption aria-hidden="true">Body Radius’s and Position Vectors</figcaption>
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|
||
<p>Here is a more detailed view of the eclipse that will make it easier to explain what is going on. There are 2 Position vectors, and 2 radius that need to be known for simple eclipse determination. More advanced cases where the atmosphere of the body your orbiting can significantly affect the Umbra and Penumbra, and other bodies could also potentially block the Sun. However, we will keep it simple for this example since they have minimal effect on the ISS’s orbit. <code style="color:#0b7285">Rsun</code> and <code style="color:#c92a2a">Rbody</code> are the radius of the Sun and Body (In this case Earth), respectively. <code style="color:#5f3dc4">r_sun_body</code> is a vector from the center of the Sun to the center of the target body. For this example I will only be using one vector, but for more rigorous eclipse determination it is important to calculate the ephemeris at least once a day since it does significantly change over the course of a year. The reason that I am ignoring it at the moment is because there is currently no good way to calculate <a href="https://ssd.jpl.nasa.gov/?ephemerides">Ephemerides</a> in Julia but the package is being worked on so I may revisit this and do a more rigorous analysis in the future. <code style="color:#5c940d">r_body_sc</code> is a position vector from the center of the body being orbited, to the center of our spacecraft.</p>
|
||
<h2 id="the-code">The Code</h2>
|
||
<div class="layout-chunk" data-layout="l-body">
|
||
<details>
|
||
<summary>
|
||
Show code
|
||
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|
||
<div class="sourceCode" id="cb1"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> Unitful</span>
|
||
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> LinearAlgebra</span>
|
||
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> SatelliteToolbox</span>
|
||
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> Plots</span>
|
||
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> Colors</span>
|
||
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a>theme(<span class="op">:</span>ggplot2)</span></code></pre></div>
|
||
</details>
|
||
</div>
|
||
<p>To get the orbit for the ISS, I used a <a href="https://en.wikipedia.org/wiki/Two-line_element_set">Two-Line Element</a> which is a data format for explaining orbits. The US Joint Space Operations Center makes these widely available, but <a href="https://live.ariss.org/tle/" class="uri">https://live.ariss.org/tle/</a> makes the TLE for the ISS way more accessible <span class="citation" data-cites="ariss">(<a href="#ref-ariss" role="doc-biblioref"><span>“<span>ARISS</span> <span>TLE</span>,”</span> n.d.</a>)</span>. The Julia Package <a href="https://github.com/JuliaSpace/SatelliteToolbox.jl">SatelliteToolbox.jl</a> makes it super easy to turn a TLE into an orbit that can be propagated. Simply putting the TLE in a string and using the <code>tle</code> string macro like below, we now have access to the information to start making our ISS orbit.</p>
|
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<div class="layout-chunk" data-layout="l-body">
|
||
<div class="sourceCode" id="cb2"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>ISS <span class="op">=</span> tle<span class="st">"""</span></span>
|
||
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="st">ISS (ZARYA)</span></span>
|
||
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a><span class="st">1 25544U 98067A 21103.84943184 .00000176 00000-0 11381-4 0 9990</span></span>
|
||
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="st">2 25544 51.6434 300.9481 0002858 223.8443 263.8789 15.48881793278621</span></span>
|
||
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a><span class="st">"""</span></span></code></pre></div>
|
||
<pre><code>1-element Vector{TLE}:
|
||
TLE: ISS (ZARYA) (Epoch = 2021-04-13T20:23:10.911)</code></pre>
|
||
</div>
|
||
<p>Now that we have the TLE, we can pass that into SatelliteToolbox’s orbit propagator. Before propagating the orbit, we need to have a range of time steps to pass into the propagator. The TLE gives the mean motion, n, which is the revolutions per day, so using that, we can calculate the amount of time required for one orbit, which is all that we’re worried about for this analysis. The propagator returns a tuple containing the Orbital elements, a position vector with units meters, and a velocity vector with units meters per second. For this analysis were only worried about the position vector.</p>
|
||
<div class="layout-chunk" data-layout="l-body">
|
||
<div class="sourceCode" id="cb4"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>ISS[<span class="fl">1</span>].n</span></code></pre></div>
|
||
</div>
|
||
<div class="layout-chunk" data-layout="l-body">
|
||
<div class="sourceCode" id="cb5"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>orbit <span class="op">=</span> init_orbit_propagator(<span class="dt">Val</span>(<span class="op">:</span>twobody)<span class="op">,</span> ISS[<span class="fl">1</span>])<span class="op">;</span></span>
|
||
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>time <span class="op">=</span> <span class="fl">0</span><span class="op">:</span><span class="fl">0.1</span><span class="op">:</span>((<span class="fl">24</span> <span class="op">/</span> ISS[<span class="fl">1</span>].n) <span class="op">.*</span> <span class="fl">60</span> <span class="op">*</span> <span class="fl">60</span>)<span class="op">;</span> <span class="co"># ISS[1].n gives the mean motion, or orbits per day.</span></span>
|
||
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a>o<span class="op">,</span> r<span class="op">,</span> v <span class="op">=</span> propagate<span class="op">!</span>(orbit<span class="op">,</span> time)<span class="op">;</span></span></code></pre></div>
|
||
</div>
|
||
<p>We just need to use the radii and vectors discussed earlier to determine if the ISS is in the penumbra or umbra. This is a lot of trigonometry and vector math that I won’t bore anyone with. However, using the diagrams above and following the code in the sunlight function, you should follow what’s happening. For a rigorous discussion, check out <span class="citation" data-cites="vallado">(<a href="#ref-vallado" role="doc-biblioref">Vallado 1997</a>)</span>.</p>
|
||
<div class="layout-chunk" data-layout="l-body">
|
||
<div class="sourceCode" id="cb6"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="kw">function</span> sunlight(Rbody<span class="op">,</span> r_sun_body<span class="op">,</span> r_body_sc)</span>
|
||
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a> Rsun <span class="op">=</span> <span class="fl">695_700</span>u<span class="st">"km"</span></span>
|
||
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a> </span>
|
||
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a> hu <span class="op">=</span> Rbody <span class="op">*</span> norm(r_sun_body) <span class="op">/</span> (Rsun <span class="op">-</span> Rbody)</span>
|
||
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a> </span>
|
||
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a> θe <span class="op">=</span> acos((r_sun_body ⋅ r_body_sc) <span class="op">/</span> (norm(r_sun_body) <span class="op">*</span> norm(r_body_sc)))</span>
|
||
<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a> θu <span class="op">=</span> atan(Rbody <span class="op">/</span> hu)</span>
|
||
<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a> du <span class="op">=</span> hu <span class="op">*</span> sin(θu) <span class="op">/</span> sin(θe <span class="op">+</span> θu)</span>
|
||
<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb6-11"><a href="#cb6-11" aria-hidden="true" tabindex="-1"></a> θp <span class="op">=</span> π <span class="op">-</span> atan(norm(r_sun_body) <span class="op">/</span> (Rsun <span class="op">+</span> Rbody))</span>
|
||
<span id="cb6-12"><a href="#cb6-12" aria-hidden="true" tabindex="-1"></a> dp <span class="op">=</span> Rbody <span class="op">*</span> sin(θp) <span class="op">/</span> cos(θe <span class="op">-</span> θp)</span>
|
||
<span id="cb6-13"><a href="#cb6-13" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb6-14"><a href="#cb6-14" aria-hidden="true" tabindex="-1"></a> S <span class="op">=</span> <span class="fl">1</span></span>
|
||
<span id="cb6-15"><a href="#cb6-15" aria-hidden="true" tabindex="-1"></a> <span class="kw">if</span> (θe <span class="op"><</span> π <span class="op">/</span> <span class="fl">2</span>) <span class="op">&&</span> (norm(r_body_sc) <span class="op"><</span> du)</span>
|
||
<span id="cb6-16"><a href="#cb6-16" aria-hidden="true" tabindex="-1"></a> S <span class="op">=</span> <span class="fl">0</span></span>
|
||
<span id="cb6-17"><a href="#cb6-17" aria-hidden="true" tabindex="-1"></a> <span class="kw">end</span></span>
|
||
<span id="cb6-18"><a href="#cb6-18" aria-hidden="true" tabindex="-1"></a> <span class="kw">if</span> (θe <span class="op"><</span> π <span class="op">/</span> <span class="fl">2</span>) <span class="op">&&</span> ((du <span class="op"><</span> norm(r_body_sc)) <span class="op">&&</span> (norm(r_body_sc) <span class="op"><</span> dp))</span>
|
||
<span id="cb6-19"><a href="#cb6-19" aria-hidden="true" tabindex="-1"></a> S <span class="op">=</span> (norm(r_body_sc .<span class="op">|></span> u<span class="st">"km"</span>) <span class="op">-</span> du) <span class="op">/</span> (dp <span class="op">-</span> du) <span class="op">|></span> ustrip</span>
|
||
<span id="cb6-20"><a href="#cb6-20" aria-hidden="true" tabindex="-1"></a> <span class="kw">end</span></span>
|
||
<span id="cb6-21"><a href="#cb6-21" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb6-22"><a href="#cb6-22" aria-hidden="true" tabindex="-1"></a> <span class="kw">return</span> S</span>
|
||
<span id="cb6-23"><a href="#cb6-23" aria-hidden="true" tabindex="-1"></a><span class="kw">end</span></span></code></pre></div>
|
||
</div>
|
||
<p>Then we can pass all the values we’ve gathered into the function we just made.</p>
|
||
<div class="layout-chunk" data-layout="l-body">
|
||
<div class="sourceCode" id="cb7"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>S <span class="op">=</span> r .<span class="op">|></span> R <span class="op">-></span> sunlight(<span class="fl">6371</span>u<span class="st">"km"</span><span class="op">,</span> [<span class="fl">0.5370</span><span class="op">,</span> <span class="fl">1.2606</span><span class="op">,</span> <span class="fl">0.5466</span>] <span class="op">.*</span> <span class="fl">1e8</span>u<span class="st">"km"</span><span class="op">,</span> R <span class="op">.*</span> u<span class="st">"m"</span>)<span class="op">;</span></span></code></pre></div>
|
||
</div>
|
||
<h2 id="plotting-the-results">Plotting the Results</h2>
|
||
<p>The <code>sunlight</code> function returns values from 0 to 1, 0 being complete darkness, 1 being complete sunlight, and anything between being the fraction of light being received. Again since the ISS has a very low orbit, the amount of time spent in the penumbra is almost insignificant.</p>
|
||
<div class="layout-chunk" data-layout="l-body-outset">
|
||
<details>
|
||
<summary>
|
||
Show code
|
||
</summary>
|
||
<div class="sourceCode" id="cb8"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Get fancy with the line color. </span></span>
|
||
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>light_range <span class="op">=</span> range(colorant<span class="st">"black"</span><span class="op">,</span> stop <span class="op">=</span> colorant<span class="st">"orange"</span><span class="op">,</span> length <span class="op">=</span> <span class="fl">101</span>)<span class="op">;</span></span>
|
||
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a>light_colors <span class="op">=</span> [light_range[unique(round(<span class="dt">Int</span><span class="op">,</span> <span class="fl">1</span> <span class="op">+</span> s <span class="op">*</span> <span class="fl">100</span>))][<span class="fl">1</span>] <span class="kw">for</span> s <span class="kw">in</span> S]<span class="op">;</span></span>
|
||
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a>plot(</span>
|
||
<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a> <span class="dt">LinRange</span>(<span class="fl">0</span><span class="op">,</span> <span class="fl">24</span><span class="op">,</span> length(S))<span class="op">,</span></span>
|
||
<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a> S <span class="op">.*</span> <span class="fl">100</span><span class="op">,</span></span>
|
||
<span id="cb8-8"><a href="#cb8-8" aria-hidden="true" tabindex="-1"></a> linewidth <span class="op">=</span> <span class="fl">5</span><span class="op">,</span></span>
|
||
<span id="cb8-9"><a href="#cb8-9" aria-hidden="true" tabindex="-1"></a> legend <span class="op">=</span> <span class="ex">false</span><span class="op">,</span></span>
|
||
<span id="cb8-10"><a href="#cb8-10" aria-hidden="true" tabindex="-1"></a> color <span class="op">=</span> light_colors<span class="op">,</span></span>
|
||
<span id="cb8-11"><a href="#cb8-11" aria-hidden="true" tabindex="-1"></a>)<span class="op">;</span></span>
|
||
<span id="cb8-12"><a href="#cb8-12" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb8-13"><a href="#cb8-13" aria-hidden="true" tabindex="-1"></a>xlabel<span class="op">!</span>(<span class="st">"Time (hr)"</span>)<span class="op">;</span></span>
|
||
<span id="cb8-14"><a href="#cb8-14" aria-hidden="true" tabindex="-1"></a>ylabel<span class="op">!</span>(<span class="st">"Sunlight (%)"</span>)<span class="op">;</span></span>
|
||
<span id="cb8-15"><a href="#cb8-15" aria-hidden="true" tabindex="-1"></a>title<span class="op">!</span>(<span class="st">"ISS Sunlight Over a Day"</span>)</span></code></pre></div>
|
||
</details>
|
||
<div class="figure"><span id="fig:sunlight-plot"></span>
|
||
<img src="iss-eclipse-determination_files/figure-html5/sunlight-plot-J1.png" alt="ISS Sunlight" width="300" data-distill-preview=1 />
|
||
<p class="caption">
|
||
Figure 1: ISS Sunlight
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<p>Looking at the plot, the vertical transition from 0% to 100% makes it pretty clear that the time in the penumbra is limited. Still, almost counterintuitively, it also looks like the ISS gets more sunlight than it does darkness. So, using the raw sunlight data, we can calculate precisely how much time is spent in each region.</p>
|
||
<p>Time in Sun:</p>
|
||
<div class="layout-chunk" data-layout="l-body">
|
||
<div class="sourceCode" id="cb9"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>sun <span class="op">=</span> length(S[S.<span class="op">==</span><span class="fl">1</span>])<span class="op">/</span>length(S) <span class="op">*</span> <span class="fl">100</span></span></code></pre></div>
|
||
<pre><code>62.03323593209401</code></pre>
|
||
</div>
|
||
<p>Time in Darkness:</p>
|
||
<div class="layout-chunk" data-layout="l-body">
|
||
<div class="sourceCode" id="cb11"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>umbra <span class="op">=</span> length(S[S.<span class="op">==</span><span class="fl">0</span>])<span class="op">/</span>length(S) <span class="op">*</span> <span class="fl">100</span></span></code></pre></div>
|
||
<pre><code>37.64408511553699</code></pre>
|
||
</div>
|
||
<p>Time in Penumbra:</p>
|
||
<div class="layout-chunk" data-layout="l-body">
|
||
<div class="sourceCode" id="cb13"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>penumbra <span class="op">=</span> <span class="fl">100</span> <span class="op">-</span> umbra <span class="op">-</span> sun</span></code></pre></div>
|
||
<pre><code>0.322678952369003</code></pre>
|
||
</div>
|
||
<p>This means that even with the ISS’s low orbit, it still gets sunlight ~62% of the time and spends almost no time in the penumbra. This would vary a few percent depending on the time of year, but in a circular orbit like the ISS, the amount of sunlight would remain pretty constant. There are other orbits like a polar orbit, lunar orbit, or highly elliptic earth orbits that can have their time in the sunlight vary widely by the time of year.</p>
|
||
<div class="sourceCode" id="cb15"><pre class="sourceCode r distill-force-highlighting-css"><code class="sourceCode r"></code></pre></div>
|
||
<div id="refs" class="references csl-bib-body hanging-indent" role="doc-bibliography">
|
||
<div id="ref-ariss" class="csl-entry" role="doc-biblioentry">
|
||
<span>“<span>ARISS</span> <span>TLE</span>.”</span> n.d. <em>Amateur Radio on the International Space Station</em>. <a href="https://live.ariss.org/tle/">https://live.ariss.org/tle/</a>.
|
||
</div>
|
||
<div id="ref-vallado" class="csl-entry" role="doc-biblioentry">
|
||
Vallado, David A. 1997. <em>Fundamentals of <span>Astrodynamics</span> and <span>Applications</span>, 2nd. Ed.</em> Edited by Wiley Larson. Dordrecht: Microcosm, Inc.
|
||
</div>
|
||
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|
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||
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|
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|
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<div class="d-appendix">
|
||
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|
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|
||
<div class="appendix-bottom">
|
||
<h3 id="references">References</h3>
|
||
<div id="references-listing"></div>
|
||
<h3 id="reuse">Reuse</h3>
|
||
<p>Text and figures are licensed under Creative Commons Attribution <a rel="license" href="https://creativecommons.org/licenses/by/4.0/">CC BY 4.0</a>. The figures that have been reused from other sources don't fall under this license and can be recognized by a note in their caption: "Figure from ...".</p>
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