Enter any two inputs and click on Calculate button
How to use this Escape Velocity Calculator 🤔
There are input fields for Constant of Gravitation \((G)\), Mass of central body \((M)\), Central body Radius \((R)\), and Escape Velocity \((v_e)\). Enter any two inputs and click on Calculate button.
The calculator uses the \( v_e = \sqrt{ \frac{ 2 G M }{ R } } \) formula, substitues given values, and calcuates the missing value.
The missing value is calcuated and displayed in the input field. Also, the caculation is displayed under the input section.
What is Escape Velocity?
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.
Calculating Escape Velocity
The escape velocity (ve) can be calculated using the formula:
\( v_e = \sqrt{ \frac{ 2 G M }{ R } } \).
In this formula, the parameters are defined as follows:
G: The gravitational constant, a universal constant with a value of approximately \(6.674 \times 10^{-11} \) N(m/kg)2.
M: The mass of the planet or celestial body from which the object is escaping, measured in kilograms (kg).
R: The radius of the planet or celestial body, measured from its center to the point of escape, in meters (m).
Input and Output Combinations of the Escape Velocity Calculator
Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.
Calculator InputsSet #1
M Mass of central body
R Central body Radius
For these given inputs,
Outputs, Formulas
We calculate the following outputs:
Escape Velocity\(v_e = \)\( \sqrt{ \frac{ 2 G M }{ R } } \)
{
"topic": "escape-velocity",
"input_types": [
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"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>"
}
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