Gravitational Potential Energy Calculator

ByDanielle Danny

Gravitational potential energy is calculated by determining the work needed to move an object from a reference point to a position within a gravitational field.

Potential Energy Calculator

Enter any 2 values to calculate the missing variable

The Gravitational Potential Energy Calculator simplifies the process of calculating the energy stored in an object due to its position in a gravitational field.

Formula:

U=−G⋅M⋅mrU = -\frac{G \cdot M \cdot m}{r}

Variable Description Unit
UU Gravitational potential energy Joules (J)
GG Gravitational constant (6.674×10−116.674 \times 10^{-11}) m3/kg⋅s2\text{m}^3/\text{kg} \cdot \text{s}^2
MM Mass of the larger body (e.g., Earth) Kilograms (kg)
mm Mass of the object Kilograms (kg)
rr Distance from the center of the larger body Meters (m)

Solved Calculations:

Example 1: Object near Earth’s Surface

Step Value Explanation
Gravitational constant (GG) 6.674×10−11 m3/kg⋅s26.674 \times 10^{-11} \, \text{m}^3/\text{kg} \cdot \text{s}^2
 Given
Mass of Earth (MM) 5.972×1024 kg5.972 \times 10^{24} \, \text{kg}
 Given
Object mass (mm) 100 kg100 \, \text{kg}
 Given
Distance from Earth’s center (rr) 6.371×106 m6.371 \times 10^{6} \, \text{m}
 Earth’s radius
Calculation U=−6.674×10−11⋅5.972×1024⋅1006.371×106U = -\frac{6.674 \times 10^{-11} \cdot 5.972 \times 10^{24} \cdot 100}{6.371 \times 10^{6}} Substitution into formula
Result U=−6.24×106 JU = -6.24 \times 10^6 \, \text{J}
 Energy stored due to gravity
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Example 2: Object in Orbit

Step Value Explanation
Gravitational constant (GG) 6.674×10−11 m3/kg⋅s26.674 \times 10^{-11} \, \text{m}^3/\text{kg} \cdot \text{s}^2
 Given
Mass of Earth (MM) 5.972×1024 kg5.972 \times 10^{24} \, \text{kg}
 Given
Object mass (mm) 500 kg500 \, \text{kg}
 Given
Distance from Earth’s center (rr) 6.771×106 m6.771 \times 10^{6} \, \text{m} Altitude included
Calculation U=−6.674×10−11⋅5.972×1024⋅5006.771×106U = -\frac{6.674 \times 10^{-11} \cdot 5.972 \times 10^{24} \cdot 500}{6.771 \times 10^{6}} Substitution into formula
Result U=−2.95×107 JU = -2.95 \times 10^7 \, \text{J}
 Energy stored in orbital position

What is the Gravitational Potential Energy ?

The Gravitational Potential Energy (GPE) Calculator is an efficient tool crafted to compute the potential energy of an object due to its position in a gravitational field.

GPE depends on the mass of the object, its height above a reference point, and the gravitational acceleration (typically 9.8 m/s² on Earth).

To use the calculator, input the object’s mass, height, and the gravitational acceleration. The formula, GPE=m×g×h\text{GPE} = m \times g \times h, where mm is mass, gg is gravitational acceleration, and hh is height, is applied to determine the energy in joules.

For instance, it can calculate the energy stored in a raised object, which can be converted to kinetic energy when it falls.

This calculator is ideal for physics students and professionals solving problems related to mechanical energy, energy transfer, or potential energy in gravitational fields. It simplifies the calculation process and reduces errors, especially in educational and engineering contexts.

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Final Words:

In conclusion, the Gravitational Potential Energy Calculator provides a precise and user-friendly solution for calculating energy due to gravity. It supports learning and practical applications, ensuring accuracy in physics-related computations.

Danielle Danny

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