{"id":2609,"date":"2026-03-01T00:40:03","date_gmt":"2026-02-28T22:40:03","guid":{"rendered":"https:\/\/science-x.net\/?page_id=2609"},"modified":"2026-03-06T18:51:38","modified_gmt":"2026-03-06T16:51:38","slug":"orbital-speed-period-calculator","status":"publish","type":"page","link":"https:\/\/science-x.net\/?page_id=2609","title":{"rendered":"Orbital Speed &amp; Period Calculator"},"content":{"rendered":"\n<div class=\"eco-tool wp-block-group\" id=\"eco-tool-orbit-9c0e4\">\n  <div class=\"eco-tool__header\">\n    <h2 class=\"eco-tool__title\">Orbital Speed &#038; Period Calculator<\/h2>\n    <p class=\"eco-tool__lead\">\n      Estimate orbital speed and period for a circular orbit around Earth, Moon, or Mars. Educational calculator.\n    <\/p>\n  <\/div>\n\n  <form class=\"eco-tool__form\" id=\"eco-orbit-form-9c0e4\" novalidate>\n    <div class=\"eco-tool__grid3\">\n      <div class=\"eco-tool__field\">\n        <label class=\"eco-tool__label\" for=\"eco-orbit-body-9c0e4\">Central body<\/label>\n        <select class=\"eco-tool__input\" id=\"eco-orbit-body-9c0e4\">\n          <option value=\"earth\" selected>Earth<\/option>\n          <option value=\"moon\">Moon<\/option>\n          <option value=\"mars\">Mars<\/option>\n        <\/select>\n        <div class=\"eco-tool__hint\">Uses standard gravitational parameter (\u03bc).<\/div>\n      <\/div>\n\n      <div class=\"eco-tool__field\">\n        <label class=\"eco-tool__label\" for=\"eco-orbit-alt-9c0e4\">Altitude above surface (km)<\/label>\n        <input class=\"eco-tool__input\" id=\"eco-orbit-alt-9c0e4\" type=\"number\" min=\"0\" step=\"1\" value=\"400\" inputmode=\"numeric\" \/>\n        <div class=\"eco-tool__hint\">Example: ~400 km (ISS altitude).<\/div>\n      <\/div>\n\n      <div class=\"eco-tool__field\">\n        <label class=\"eco-tool__label\" for=\"eco-orbit-unit-9c0e4\">Output units<\/label>\n        <select class=\"eco-tool__input\" id=\"eco-orbit-unit-9c0e4\">\n          <option value=\"metric\" selected>km\/s + minutes<\/option>\n          <option value=\"si\">m\/s + seconds<\/option>\n        <\/select>\n        <div class=\"eco-tool__hint\">Choose your preferred units.<\/div>\n      <\/div>\n\n      <div class=\"eco-tool__field\">\n        <label class=\"eco-tool__label\" for=\"eco-orbit-incl-9c0e4\">Inclination (optional)<\/label>\n        <select class=\"eco-tool__input\" id=\"eco-orbit-incl-9c0e4\">\n          <option value=\"none\" selected>Ignore (circular orbit only)<\/option>\n          <option value=\"leo\">Typical LEO (mostly)<\/option>\n          <option value=\"polar\">Polar orbit<\/option>\n        <\/select>\n        <div class=\"eco-tool__hint\">Does not change speed; adds interpretation.<\/div>\n      <\/div>\n\n      <div class=\"eco-tool__field\">\n        <label class=\"eco-tool__label\" for=\"eco-orbit-round-9c0e4\">Rounding<\/label>\n        <select class=\"eco-tool__input\" id=\"eco-orbit-round-9c0e4\">\n          <option value=\"2\" selected>2 decimals<\/option>\n          <option value=\"3\">3 decimals<\/option>\n          <option value=\"0\">Whole numbers<\/option>\n        <\/select>\n        <div class=\"eco-tool__hint\">For cleaner display.<\/div>\n      <\/div>\n\n      <div class=\"eco-tool__field\">\n        <label class=\"eco-tool__label\" for=\"eco-orbit-ref-9c0e4\">Reference note<\/label>\n        <select class=\"eco-tool__input\" id=\"eco-orbit-ref-9c0e4\">\n          <option value=\"basic\" selected>Basic<\/option>\n          <option value=\"advanced\">More context<\/option>\n        <\/select>\n        <div class=\"eco-tool__hint\">Shows a short explanation.<\/div>\n      <\/div>\n    <\/div>\n\n    <div class=\"eco-tool__actions\">\n      <button type=\"button\" class=\"wp-element-button eco-tool__btn\" id=\"eco-orbit-calc-9c0e4\">Calculate<\/button>\n      <button type=\"button\" class=\"wp-element-button eco-tool__btn eco-tool__btn--ghost\" id=\"eco-orbit-reset-9c0e4\">Reset<\/button>\n      <div class=\"eco-tool__error\" id=\"eco-orbit-error-9c0e4\" aria-live=\"polite\"><\/div>\n    <\/div>\n  <\/form>\n\n  <div class=\"eco-tool__result\" id=\"eco-orbit-result-9c0e4\" hidden>\n    <h3 class=\"eco-tool__subtitle\">Result<\/h3>\n\n    <div class=\"eco-tool__cards\">\n      <div class=\"eco-tool__card\">\n        <div class=\"eco-tool__metric-label\">Orbital speed<\/div>\n        <div class=\"eco-tool__metric-value\" id=\"eco-orbit-speed-9c0e4\">\u2014<\/div>\n        <div class=\"eco-tool__metric-sub\" id=\"eco-orbit-speed-sub-9c0e4\"><\/div>\n      <\/div>\n\n      <div class=\"eco-tool__card\">\n        <div class=\"eco-tool__metric-label\">Orbital period<\/div>\n        <div class=\"eco-tool__metric-value\" id=\"eco-orbit-period-9c0e4\">\u2014<\/div>\n        <div class=\"eco-tool__metric-sub\" id=\"eco-orbit-period-sub-9c0e4\"><\/div>\n      <\/div>\n    <\/div>\n\n    <div class=\"eco-tool__card eco-tool__card--wide\">\n      <div class=\"eco-tool__metric-label\">Orbit radius<\/div>\n      <div class=\"eco-tool__metric-value\" id=\"eco-orbit-radius-9c0e4\">\u2014<\/div>\n      <div class=\"eco-tool__metric-sub\" id=\"eco-orbit-note-9c0e4\"><\/div>\n    <\/div>\n\n    <p class=\"eco-tool__note\">\n      Model: circular orbit. Formulas: v = \u221a(\u03bc \/ r), period T = 2\u03c0 \u221a(r\u00b3 \/ \u03bc).\n    <\/p>\n  <\/div>\n<\/div>\n\n<style>\n.eco-tool{border:1px solid rgba(0,0,0,.12);border-radius:12px;padding:16px}\n.eco-tool__header{margin-bottom:12px}\n.eco-tool__title{margin:0 0 8px}\n.eco-tool__lead{margin:0;opacity:.9}\n.eco-tool__form{margin-top:12px}\n.eco-tool__grid3{display:grid;grid-template-columns:1fr;gap:16px}\n@media(min-width:860px){.eco-tool__grid3{grid-template-columns:1fr 1fr 1fr}}\n.eco-tool__field{display:flex;flex-direction:column;gap:6px}\n.eco-tool__label{font-weight:600}\n.eco-tool__input{width:100%;height:44px;padding:0 12px;border:1px solid rgba(0,0,0,.2);border-radius:10px;background:#fff;box-sizing:border-box;font:inherit}\n.eco-tool select.eco-tool__input{appearance:none;-webkit-appearance:none;line-height:44px;padding-right:40px;background-image:linear-gradient(45deg, transparent 50%, rgba(0,0,0,.60) 50%),linear-gradient(135deg, rgba(0,0,0,.60) 50%, transparent 50%);background-position:calc(100% - 18px) 50%,calc(100% - 12px) 50%;background-size:6px 6px;background-repeat:no-repeat}\n.eco-tool__hint{font-size:.92em;opacity:.78;min-height:38px}\n.eco-tool__actions{display:flex;flex-wrap:wrap;gap:10px;align-items:center;margin-top:16px}\n.eco-tool__btn{padding:10px 22px}\n.eco-tool__btn--ghost{background:transparent!important;border:1px solid rgba(0,0,0,.2)!important}\n.eco-tool__btn--ghost:hover,.eco-tool__btn--ghost:focus{background:rgba(0,0,0,.06)!important;border-color:rgba(0,0,0,.35)!important}\n.eco-tool__error{min-height:1.2em;font-weight:600;flex:1 1 240px}\n.eco-tool__result{margin-top:16px}\n.eco-tool__subtitle{margin:0 0 10px}\n.eco-tool__cards{display:grid;gap:10px;grid-template-columns:1fr}\n@media(min-width:860px){.eco-tool__cards{grid-template-columns:1fr 1fr}}\n.eco-tool__card{border:1px solid rgba(0,0,0,.12);border-radius:12px;padding:12px}\n.eco-tool__card--wide{margin-top:10px}\n.eco-tool__metric-label{opacity:.85;font-weight:600}\n.eco-tool__metric-value{font-size:1.6em;font-weight:800;margin-top:6px;line-height:1.1}\n.eco-tool__metric-sub{opacity:.85;margin-top:6px}\n.eco-tool__note{margin:10px 0 0;opacity:.9}\n<\/style>\n\n<script>\n(function(){\n  const S=\"9c0e4\";\n  const el=id=>document.getElementById(id+\"-\"+S);\n\n  const bodyEl = el(\"eco-orbit-body\");\n  const altEl  = el(\"eco-orbit-alt\");\n  const unitEl = el(\"eco-orbit-unit\");\n  const inclEl = el(\"eco-orbit-incl\");\n  const roundEl= el(\"eco-orbit-round\");\n  const refEl  = el(\"eco-orbit-ref\");\n\n  const calcBtn= el(\"eco-orbit-calc\");\n  const resetBtn=el(\"eco-orbit-reset\");\n  const errEl  = el(\"eco-orbit-error\");\n\n  const resEl  = el(\"eco-orbit-result\");\n  const speedEl= el(\"eco-orbit-speed\");\n  const speedSub=el(\"eco-orbit-speed-sub\");\n  const periodEl=el(\"eco-orbit-period\");\n  const periodSub=el(\"eco-orbit-period-sub\");\n  const radiusEl=el(\"eco-orbit-radius\");\n  const noteEl = el(\"eco-orbit-note\");\n\n  \/\/ \u03bc in km^3\/s^2, radius in km\n  const BODIES = {\n    earth: { name:\"Earth\", mu: 398600.4418, r: 6371.0 },\n    moon:  { name:\"Moon\",  mu:   4902.8001, r: 1737.4 },\n    mars:  { name:\"Mars\",  mu:  42828.3752, r: 3389.5 }\n  };\n\n  function setError(msg){ errEl.textContent = msg || \"\"; }\n  function roundTo(x, d){\n    if (d === 0) return Math.round(x);\n    const p = Math.pow(10, d);\n    return Math.round(x * p) \/ p;\n  }\n\n  function calculate(){\n    setError(\"\");\n\n    const alt = Number(altEl.value);\n    if (!Number.isFinite(alt) || alt < 0){\n      setError(\"Please enter a valid altitude (km \u2265 0).\");\n      resEl.hidden = true;\n      return;\n    }\n\n    const body = BODIES[bodyEl.value];\n    const r = body.r + alt; \/\/ km\n    const v = Math.sqrt(body.mu \/ r); \/\/ km\/s\n    const T = 2 * Math.PI * Math.sqrt((r*r*r) \/ body.mu); \/\/ seconds\n\n    const d = Number(roundEl.value);\n    const vR = roundTo(v, d);\n    const rR = roundTo(r, 1);\n\n    if (unitEl.value === \"si\"){\n      const vms = vR * 1000; \/\/ m\/s\n      speedEl.textContent = vms.toLocaleString() + \" m\/s\";\n      speedSub.textContent = `${body.name} \u2022 altitude ${Math.round(alt).toLocaleString()} km`;\n\n      const Ts = roundTo(T, 0);\n      periodEl.textContent = Ts.toLocaleString() + \" s\";\n      periodSub.textContent = `\u2248 ${roundTo(T\/60, 1).toLocaleString()} minutes`;\n\n      radiusEl.textContent = rR.toLocaleString() + \" km\";\n    } else {\n      speedEl.textContent = vR.toLocaleString() + \" km\/s\";\n      speedSub.textContent = `${body.name} \u2022 altitude ${Math.round(alt).toLocaleString()} km`;\n\n      const Tmin = roundTo(T\/60, 1);\n      periodEl.textContent = Tmin.toLocaleString() + \" minutes\";\n      periodSub.textContent = `\u2248 ${roundTo(T\/3600, 2).toLocaleString()} hours`;\n\n      radiusEl.textContent = rR.toLocaleString() + \" km\";\n    }\n\n    \/\/ Notes\n    const incl = inclEl.value;\n    const adv = refEl.value === \"advanced\";\n    let n = \"Circular orbit assumption. Real orbits can be elliptical and require corrections.\";\n    if (incl === \"polar\") n = \"Polar orbit note: inclination doesn\u2019t change speed for a circular orbit at the same radius.\";\n    if (incl === \"leo\") n = \"LEO note: low Earth orbits typically range from ~160\u20132,000 km altitude.\";\n    if (adv) n += \" This ignores atmosphere drag, J2 perturbations, and non-circular trajectories.\";\n\n    noteEl.textContent = n;\n    resEl.hidden = false;\n  }\n\n  function reset(){\n    setError(\"\");\n    bodyEl.value = \"earth\";\n    altEl.value = \"400\";\n    unitEl.value = \"metric\";\n    inclEl.value = \"none\";\n    roundEl.value = \"2\";\n    refEl.value = \"basic\";\n    resEl.hidden = true;\n  }\n\n  calcBtn.addEventListener(\"click\", calculate);\n  resetBtn.addEventListener(\"click\", reset);\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Orbital Speed &#038; Period Calculator Estimate orbital speed and period for a circular orbit around Earth, Moon, or Mars. Educational calculator. Central body EarthMoonMars Uses standard gravitational parameter (\u03bc). Altitude&hellip;<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":2295,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_sitemap_exclude":false,"_sitemap_priority":"","_sitemap_frequency":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/science-x.net\/index.php?rest_route=\/wp\/v2\/pages\/2609"}],"collection":[{"href":"https:\/\/science-x.net\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/science-x.net\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/science-x.net\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/science-x.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2609"}],"version-history":[{"count":1,"href":"https:\/\/science-x.net\/index.php?rest_route=\/wp\/v2\/pages\/2609\/revisions"}],"predecessor-version":[{"id":2610,"href":"https:\/\/science-x.net\/index.php?rest_route=\/wp\/v2\/pages\/2609\/revisions\/2610"}],"up":[{"embeddable":true,"href":"https:\/\/science-x.net\/index.php?rest_route=\/wp\/v2\/pages\/2295"}],"wp:attachment":[{"href":"https:\/\/science-x.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2609"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}