Calculator Form
Example Data Table
| Scenario | Mass 1 | Mass 2 | Distance | Force |
|---|---|---|---|---|
| Small laboratory objects | 10 kg | 20 kg | 2 m | 3.337150e-9 N |
| Heavy equipment bodies | 500 kg | 1200 kg | 5 m | 1.601832e-6 N |
| Earth and 1000 kg object | 5.972e24 kg | 1000 kg | 6,371,000 m | 9,819.973426 N |
These rows illustrate the inverse square effect. Large masses create stronger attraction, but increasing distance rapidly weakens force.
Formula Used
F = G × m₁ × m₂ / r²
m₁ = F × r² / (G × m₂)
m₂ = F × r² / (G × m₁)
r = √(G × m₁ × m₂ / F)
Where:
- F = gravitational force in newtons
- G = gravitational constant, usually 6.67430 × 10-11 N·m²/kg²
- m₁ and m₂ = object masses in kilograms
- r = center-to-center distance in meters
The result follows an inverse square pattern. If distance doubles, the force becomes one fourth as large, assuming both masses stay unchanged.
How to Use This Calculator
- Select which variable you want the calculator to solve.
- Enter the known values for the remaining fields.
- Choose matching units for both masses, the distance, and the force.
- Keep the default gravitational constant unless you need a custom value.
- Press Calculate Now to display the result above the form.
- Review the graph, summary table, accelerations, and potential energy values.
- Use the CSV or PDF buttons to export the current result.
Frequently Asked Questions
1) What equation does this calculator use?
It uses Newton’s law of universal gravitation: force equals the gravitational constant multiplied by both masses, then divided by the square of the center-to-center distance.
2) Why does force drop so quickly with distance?
Gravity follows an inverse square rule. When distance grows, the denominator grows as distance squared, so even modest separation increases reduce force strongly.
3) Can I solve for a missing mass?
Yes. Choose Mass 1 or Mass 2 in the Solve For menu, then enter the known force, known mass, and center-to-center distance.
4) Should I enter surface distance or center distance?
Use center-to-center distance. For spheres, that means radius one plus radius two plus any gap between their surfaces.
5) Does the tool support very large astronomy values?
Yes. It supports scientific notation and large-scale units such as Earth masses, solar masses, kilometers, miles, and astronomical units.
6) Why are the two accelerations different?
Both bodies feel equal gravitational force, but acceleration equals force divided by mass. The lighter body therefore accelerates more than the heavier one.
7) Does this include relativistic corrections?
No. This calculator uses classical Newtonian gravitation. It works well for most engineering, classroom, and general physics applications.
8) What do the export buttons save?
They save the current summary metrics shown in the result section. CSV is useful for spreadsheets, while PDF is useful for reports and sharing.