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{
  "topic": "escape-velocity",
  "input_types": [
    "constant",
    "float",
    "float",
    "float"
  ],
  "input_labels": [
    "G",
    "M",
    "R",
    "v_e"
  ],
  "input_descriptions": [
    "Constant of Gravitation",
    "Mass of central body",
    "Central body Radius",
    "Escape Velocity"
  ],
  "input_units": [
    "m<sup>3</sup>kg<sup>-1</sup>s<sup>-2</sup>",
    "kg",
    "m",
    "m/s"
  ],
  "formula_mathjax": "\\( v_e = \\sqrt{ \\frac{ 2 G M }{ R } } \\)",
  "input_values": [
    "6.674e−11",
    "",
    "",
    ""
  ],
  "input_pre_msg": "Enter any two inputs and click on Calculate button",
  "type": "Calculate",
  "title": "Escape Velocity Calculator",
  "description": "Calculate the escape velocity needed for an object to break free from a celestial body's gravitational pull using our Escape Velocity Calculator. Input the mass and radius of the celestial body to get instant results. Ideal for students, teachers, and astronomy enthusiasts.",
  "category": "Rocketry",
  "template": "physics",
  "formulas": [
    {
      "parameters": [
        "M",
        "R"
      ],
      "outputs": [
        {
          "label": "v_e",
          "formula": " Math.sqrt(( 2* 6.674e-11 * M )/ R ) ",
          "formula_mathjax": "\\( \\sqrt{ \\frac{ 2 G M }{ R } } \\)"
        }
      ]
    }
  ],
  "content": "<h2>What is Escape Velocity?</h2><p>Escape velocity is the minimum speed that an object needs to escape the gravitational pull of a planet or any other celestial body without further propulsion. If an object reaches this speed, it can move away from the planet indefinitely.</p><h2>Calculating Escape Velocity</h2><p>The escape velocity (<strong>v<sub>e</sub></strong>) can be calculated using the formula:</p><p class=\"formula_highlite\">\\( v_e = \\sqrt{ \\frac{ 2 G M }{ R } } \\).</p><p>In this formula, the parameters are defined as follows:</p><ul><li><strong>G</strong>: The gravitational constant, a universal constant with a value of approximately \\(6.674 \\times 10^{-11} \\) N(m/kg)<sup>2</sup>.</li><li><strong>M</strong>: The mass of the planet or celestial body from which the object is escaping, measured in kilograms (kg).</li><li><strong>R</strong>: The radius of the planet or celestial body, measured from its center to the point of escape, in meters (m).</li></ul><br><h2>Input and Output Combinations of the Escape Velocity Calculator</h2><p>Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.</p><div class=\"formula_sets\"><div class=\"formula_set set_1\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #1</span><ul class=\"given\"><li><span class=\"input\">M</span> Mass of central body</li><li><span class=\"input\">R</span> Central body Radius</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Escape Velocity</span><span class=\"output\">\\(v_e = \\)\\( \\sqrt{ \\frac{ 2 G M }{ R } } \\)</span></li></ul></div></div><br><br><h2>Examples</h2><br><h2>Input and Output Combinations of the Escape Velocity Calculator</h2><p>Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.</p><div class=\"formula_sets\"><div class=\"formula_set set_1\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #1</span><ul class=\"given\"><li><span class=\"input\">M</span> Mass of central body</li><li><span class=\"input\">R</span> Central body Radius</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Escape Velocity</span><span class=\"output\">\\(v_e = \\)\\( \\sqrt{ \\frac{ 2 G M }{ R } } \\)</span></li></ul></div></div><br><br><h2>Examples</h2><br><h2>Input and Output Combinations of the Escape Velocity Calculator</h2><p>Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.</p><div class=\"formula_sets\"><div class=\"formula_set set_1\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #1</span><ul class=\"given\"><li><span class=\"input\">M</span> Mass of central body</li><li><span class=\"input\">R</span> Central body Radius</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Escape Velocity</span><span class=\"output\">\\(v_e = \\)\\( \\sqrt{ \\frac{ 2 G M }{ R } } \\)</span></li></ul></div></div><br><br><h2>Examples</h2><br><h2>Input and Output Combinations of the Escape Velocity Calculator</h2><p>Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.</p><div class=\"formula_sets\"><div class=\"formula_set set_1\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #1</span><ul class=\"given\"><li><span class=\"input\">M</span> Mass of central body</li><li><span class=\"input\">R</span> Central body Radius</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Escape Velocity</span><span class=\"output\">\\(v_e = \\)\\( \\sqrt{ \\frac{ 2 G M }{ R } } \\)</span></li></ul></div></div><br><br><h2>Examples</h2><br><h2>Input and Output Combinations of the Escape Velocity Calculator</h2><p>Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.</p><div class=\"formula_sets\"><div class=\"formula_set set_1\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #1</span><ul class=\"given\"><li><span class=\"input\">M</span> Mass of central body</li><li><span class=\"input\">R</span> Central body Radius</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Escape Velocity</span><span class=\"output\">\\(v_e = \\)\\( \\sqrt{ \\frac{ 2 G M }{ R } } \\)</span></li></ul></div></div><br><br><h2>Examples</h2><br><h2>Input and Output Combinations of the Escape Velocity Calculator</h2><p>Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.</p><div class=\"formula_sets\"><div class=\"formula_set set_1\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #1</span><ul class=\"given\"><li><span class=\"input\">M</span> Mass of central body</li><li><span class=\"input\">R</span> Central body Radius</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Escape Velocity</span><span class=\"output\">\\(v_e = \\)\\( \\sqrt{ \\frac{ 2 G M }{ R } } \\)</span></li></ul></div></div><br><br><h2>Examples</h2><br><h2>Input and Output Combinations of the Escape Velocity Calculator</h2><p>Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.</p><div class=\"formula_sets\"><div class=\"formula_set set_1\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #1</span><ul class=\"given\"><li><span class=\"input\">M</span> Mass of central body</li><li><span class=\"input\">R</span> Central body Radius</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Escape Velocity</span><span class=\"output\">\\(v_e = \\)\\( \\sqrt{ \\frac{ 2 G M }{ R } } \\)</span></li></ul></div></div><br><br><h2>Examples</h2>"
}