Calculate the Weight of the Moon: Mass & Gravity Calculator
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Calculate the Weight of the Moon: Mass & Gravity Calculator
This professional scientific tool allows you to calculate the weight of the moon (mass) based on radius and density, determine surface gravity, and convert weight from Earth to Lunar equivalents.
Calculated Mass of the Moon
7.346e+22 kg
Derived from Volume × Density
Surface Gravity
1.62 m/s²
Weight on this Moon
24.77 lbs
Escape Velocity
2.38 km/s
Weight Comparison: Earth vs. Calculated Moon
Figure 1: Comparison of reference weight on Earth versus the calculated weight on the Moon.
What is Calculate the Weight of the Moon?
When people ask to calculate the weight of the moon, they are generally referring to one of two distinct physical concepts: the mass of the Moon itself, or the weight of an object (like a human) if they were standing on the Moon's surface.
In physics, "weight" is a force generated by gravity acting on mass. Since the Moon is in freefall orbit around the Earth, it doesn't have a "weight" in the traditional sense unless it were resting on a larger surface. However, it has a tremendous mass—approximately 7.35 × 10²² kilograms. Understanding how to calculate the weight of the moon involves applying Newton's Law of Universal Gravitation and understanding the relationship between volume, density, and gravitational acceleration.
This calculator is designed for students, astronomers, and science enthusiasts who want to explore how changes in radius and density affect the total mass and surface gravity of a lunar body. It resolves common misconceptions by clearly distinguishing between mass (intrinsic matter) and weight (gravitational force).
Calculate the Weight of the Moon: Formula and Explanation
To calculate the weight of the moon (specifically its mass), we treat the Moon as a sphere. The calculation is a two-step process involving geometry and density.
Step 1: Calculate Volume
First, we calculate the volume of the sphere using the radius:
V = (4/3) × π × r³
Step 2: Calculate Mass
Once volume is known, we multiply by the mean density to find the mass:
M = V × ρ
Step 3: Calculate Surface Gravity
To find out what things weigh on this moon, we calculate the acceleration due to gravity:
g = (G × M) / r²
Table 1: Variables used to calculate the weight of the moon
| Variable |
Meaning |
Unit |
Typical Moon Value |
| r |
Radius |
Meters (m) |
1.737 × 10⁶ m |
| ρ (rho) |
Mean Density |
kg/m³ |
3344 kg/m³ |
| M |
Mass |
Kilograms (kg) |
7.346 × 10²² kg |
| G |
Gravitational Constant |
m³/(kg·s²) |
6.674 × 10⁻¹¹ |
Practical Examples (Real-World Use Cases)
Example 1: The Standard Moon
Let's use the standard scientific values to calculate the weight of the moon.
- Radius: 1737.4 km
- Density: 3344 kg/m³
Result: The mass comes out to approximately 7.35 × 10²² kg. The surface gravity is 1.62 m/s². If an astronaut weighs 180 lbs on Earth, they would weigh approximately 29.7 lbs on the Moon.
Example 2: A Dense Iron Moon
Imagine a theoretical moon of the same size but made entirely of iron (Density ~7874 kg/m³).
- Radius: 1737.4 km
- Density: 7874 kg/m³
Result: The mass would more than double to roughly 1.73 × 10²³ kg. Surface gravity would jump to 3.82 m/s². That same 180 lb astronaut would now weigh roughly 70 lbs on this dense moon.
How to Use This Moon Weight Calculator
- Enter the Moon Radius: Input the radius in kilometers. The default is Earth's Moon (1737.4 km).
- Enter Mean Density: Input the density in kg/m³. Higher density implies a rocky or metallic composition.
- Enter Reference Earth Weight: Input your weight (or any object's weight) in pounds to see the conversion.
- Analyze Results:
- Calculated Mass: The total amount of matter in the moon.
- Surface Gravity: The acceleration force at the surface (Earth is 9.81 m/s²).
- Weight on this Moon: Your adjusted weight due to the lower gravity.
Key Factors That Affect Moon Weight Results
When you calculate the weight of the moon, several physical factors dramatically influence the outcome.
1. Radius (Volume)
Since volume increases with the cube of the radius, even a small increase in size leads to a massive increase in mass. A moon twice as wide has eight times the volume.
2. Density and Composition
The material composition defines density. A moon made of ice (density ~900 kg/m³) will have far less mass and gravity than a moon made of rock or iron, even if they are the same size.
3. Gravitational Compression
For very large bodies, the core density is higher than the surface density due to the weight of overlying layers compressing the center. This calculator uses "Mean Density" to simplify this complex factor.
4. Surface Gravity vs. Mass
Interestingly, you can have a high mass but low surface gravity if the radius is huge (like a gas giant). Conversely, a small, ultra-dense object (like a neutron star) has immense gravity.
5. Centrifugal Force
If the moon rotates rapidly, the effective weight at the equator is slightly less than at the poles. This calculator assumes a non-rotating sphere for simplicity.
6. Tidal Forces
When calculating the effective weight of an object on a moon, the tidal pull from the parent planet (like Earth) can theoretically reduce the weight slightly on the near and far sides, though the effect is minimal for human-scale objects.
Frequently Asked Questions (FAQ)
1. Why is the weight on the Moon 1/6th of Earth?
Because the Moon's mass is about 1.2% of Earth's, and its radius is about 27% of Earth's. Putting these into the gravity formula results in a surface acceleration of 1.62 m/s², which is roughly 16.5% (or 1/6th) of Earth's 9.81 m/s².
2. Can I use this to calculate the weight of other planets?
Yes. If you input the radius and density of Mars or Jupiter, the tool will correctly calculate the weight of the moon equivalent (or planet equivalent) for those bodies.
3. Does my mass change on the Moon?
No. Your mass (the amount of matter in your body) remains exactly the same. Only your weight (the force of gravity pulling on you) changes.
4. What unit is used for Mass?
Mass is measured in Kilograms (kg). The calculator uses scientific notation (e.g., 7.35e+22) because the numbers are astronomically large.
5. How accurate is the density value?
The default 3344 kg/m³ is the precise mean density of Earth's Moon determined by orbital missions. Changing this allows you to simulate hypothetical moons.
6. What is Escape Velocity?
Escape velocity is the speed required to break free from the moon's gravity without further propulsion. For Earth's Moon, it is about 2.38 km/s.
7. Is weight calculated in pounds or kilograms?
The "Reference Weight" input is labeled in lbs, but the math works proportionally. If you enter kg, the output "Weight on Moon" will also be in kg.
8. Why do I need to calculate the weight of the moon?
Calculating the mass is essential for orbital mechanics. It determines how fast a satellite must orbit, the strength of tides on Earth, and the fuel required for lunar landing missions.
Related Tools and Internal Resources
Explore more astronomical and physics calculators:
// GLOBAL CONSTANTS (using var)
var G = 6.67430e-11; // Gravitational Constant
var PI = Math.PI;
// DOM ELEMENTS
var elRadius = document.getElementById('moonRadius');
var elDensity = document.getElementById('moonDensity');
var elWeight = document.getElementById('earthWeight');
var elMassResult = document.getElementById('moonMassResult');
var elGravityResult = document.getElementById('surfaceGravityResult');
var elMoonWeightResult = document.getElementById('moonWeightResult');
var elEscapeResult = document.getElementById('escapeVelocityResult');
var elRadiusError = document.getElementById('radiusError');
var elDensityError = document.getElementById('densityError');
var elWeightError = document.getElementById('weightError');
var ctx = document.getElementById('gravityChart').getContext('2d');
var chartObj = null;
// INITIALIZATION
window.onload = function() {
calculateMoon();
};
// CALCULATION LOGIC
function calculateMoon() {
// 1. Get Inputs
var radiusKm = parseFloat(elRadius.value);
var density = parseFloat(elDensity.value);
var earthWeight = parseFloat(elWeight.value);
// 2. Validate
var isValid = true;
if (isNaN(radiusKm) || radiusKm <= 0) {
elRadiusError.style.display = 'block';
isValid = false;
} else {
elRadiusError.style.display = 'none';
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if (isNaN(density) || density <= 0) {
elDensityError.style.display = 'block';
isValid = false;
} else {
elDensityError.style.display = 'none';
}
if (isNaN(earthWeight) || earthWeight < 0) {
elWeightError.style.display = 'block';
isValid = false;
} else {
elWeightError.style.display = 'none';
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if (!isValid) return;
// 3. Perform Math
// Convert radius to meters
var radiusM = radiusKm * 1000;
// Volume V = 4/3 * pi * r^3
var volume = (4/3) * PI * Math.pow(radiusM, 3);
// Mass M = Density * Volume
var mass = density * volume;
// Surface Gravity g = (G * M) / r^2
var gravity = (G * mass) / Math.pow(radiusM, 2);
// Escape Velocity v = sqrt(2 * G * M / r)
var escapeVel = Math.sqrt((2 * G * mass) / radiusM);
// Weight on Moon = (Earth Weight / 9.80665) * Moon Gravity
var moonWeight = (earthWeight / 9.80665) * gravity;
// 4. Update UI
elMassResult.innerText = mass.toExponential(3) + " kg";
elGravityResult.innerText = gravity.toFixed(2) + " m/s²";
elMoonWeightResult.innerText = moonWeight.toFixed(2) + " lbs";
elEscapeResult.innerText = (escapeVel / 1000).toFixed(2) + " km/s";
// 5. Update Chart
drawChart(earthWeight, moonWeight);
}
// RESET FUNCTION
function resetCalculator() {
elRadius.value = 1737.4;
elDensity.value = 3344;
elWeight.value = 150;
elRadiusError.style.display = 'none';
elDensityError.style.display = 'none';
elWeightError.style.display = 'none';
calculateMoon();
}
// COPY RESULTS FUNCTION
function copyResults() {
var txt = "Calculated Moon Results:\n";
txt += "————————\n";
txt += "Input Radius: " + elRadius.value + " km\n";
txt += "Input Density: " + elDensity.value + " kg/m³\n";
txt += "Mass: " + elMassResult.innerText + "\n";
txt += "Surface Gravity: " + elGravityResult.innerText + "\n";
txt += "Escape Velocity: " + elEscapeResult.innerText + "\n";
txt += "Reference Earth Weight: " + elWeight.value + " lbs\n";
txt += "Equivalent Moon Weight: " + elMoonWeightResult.innerText;
var tempInput = document.createElement("textarea");
tempInput.value = txt;
document.body.appendChild(tempInput);
tempInput.select();
document.execCommand("copy");
document.body.removeChild(tempInput);
// Visual feedback
var btn = document.querySelector('.btn-copy');
var originalText = btn.innerText;
btn.innerText = "Copied!";
setTimeout(function() {
btn.innerText = originalText;
}, 1500);
}
// CHART DRAWING (Native Canvas, No Libraries)
function drawChart(earthVal, moonVal) {
var canvas = document.getElementById('gravityChart');
var width = canvas.width = canvas.offsetWidth;
var height = canvas.height = canvas.offsetHeight;
var ctx = canvas.getContext('2d');
// Clear canvas
ctx.clearRect(0, 0, width, height);
// Settings
var padding = 40;
var barWidth = Math.min(80, (width – padding * 3) / 2);
var maxValue = Math.max(earthVal, moonVal) * 1.2; // Add 20% headroom
if (maxValue === 0) maxValue = 10; // Prevent divide by zero
var zeroY = height – padding;
var chartHeight = height – padding * 2;
// Draw Axes
ctx.beginPath();
ctx.moveTo(padding, padding);
ctx.lineTo(padding, zeroY);
ctx.lineTo(width – padding, zeroY);
ctx.strokeStyle = '#ccc';
ctx.stroke();
// Bar 1: Earth
var earthBarHeight = (earthVal / maxValue) * chartHeight;
var x1 = padding + (width – padding * 2) / 4 – barWidth / 2;
var y1 = zeroY – earthBarHeight;
ctx.fillStyle = '#6c757d'; // Grey for Earth
ctx.fillRect(x1, y1, barWidth, earthBarHeight);
// Bar 2: Moon
var moonBarHeight = (moonVal / maxValue) * chartHeight;
var x2 = padding + (width – padding * 2) * 3 / 4 – barWidth / 2;
var y2 = zeroY – moonBarHeight;
ctx.fillStyle = '#004a99'; // Blue for Moon
ctx.fillRect(x2, y2, barWidth, moonBarHeight);
// Labels
ctx.fillStyle = '#333';
ctx.font = 'bold 14px sans-serif';
ctx.textAlign = 'center';
// Value Labels
ctx.fillText(earthVal.toFixed(1) + " lbs", x1 + barWidth / 2, y1 – 10);
ctx.fillText(moonVal.toFixed(1) + " lbs", x2 + barWidth / 2, y2 – 10);
// Axis Labels
ctx.font = '14px sans-serif';
ctx.fillText("Earth", x1 + barWidth / 2, zeroY + 20);
ctx.fillText("Moon (Calc)", x2 + barWidth / 2, zeroY + 20);
}
// Resize handler for chart responsiveness
window.addEventListener('resize', function() {
calculateMoon();
});