Calculator Inputs
Choose presets or enter custom macro values. Altitude can be negative for simple depth correction.
Example Data Table
This table gives common preset values used for macro comparison.
| Body | Mass, kg | Radius, m | Angular Speed, rad/s | Approx Surface Gravity, m/s² |
|---|---|---|---|---|
| Earth | 5.97219E+24 | 6,371,000 | 7.292116E-5 | 9.82029 |
| Moon | 7.34200E+22 | 1,737,400 | 2.661700E-6 | 1.62338 |
| Mars | 6.41710E+23 | 3,389,500 | 7.088218E-5 | 3.72798 |
| Venus | 4.86750E+24 | 6,051,800 | 2.992000E-7 | 8.87039 |
| Jupiter | 1.89813E+27 | 69,911,000 | 1.758500E-4 | 25.92034 |
| Saturn | 5.68340E+26 | 58,232,000 | 1.637900E-4 | 11.18640 |
Formula Used
Raw gravity above surface: g = GM / (R + h)²
Simple depth correction: gdepth = gsurface × (1 - depth / R)
Rotation correction: geff = g - ω²(R + h)cos²φ
Gravity transformation factor: T = geff target / geff source
Weight: W = mg
Fall time: t = √(2H / g)
Impact velocity: v = √(2gH)
Pendulum period: P = 2π√(L / g)
How to Use This Calculator
Select a source body and a target body. You can also choose Custom and enter your own mass, radius, and rotation speed.
Enter altitude values for both worlds. Use positive altitude above the surface. Use negative altitude for a simple internal depth estimate.
Add object mass, drop height, jump height, launch velocity, and pendulum length. Then press the calculate button.
The result box appears under the header and above the form. Use CSV or PDF buttons to save the generated output.
Gravity Transformation Macro Guide
What the Macro Means
A gravity transformation macro compares one gravity environment with another. It helps translate motion, force, and timing between worlds. The method is useful for planetary study. It is also helpful for science fiction design. It starts with the gravitational constant. Then it applies mass and radius. These two values control raw surface gravity. A large mass raises gravity. A large radius can reduce it. Altitude also matters. Gravity becomes weaker as distance increases.
Why Rotation Is Included
A rotating body creates a centrifugal reduction. The reduction is strongest near the equator. It is lower near the poles. This calculator uses latitude for that correction. The final value is called effective gravity. It is the felt downward acceleration. That value is better for weight estimates. It is also better for fall time. It gives a realistic macro comparison.
Motion Scaling
The transformation factor compares target gravity with source gravity. A factor above one means stronger target gravity. A factor below one means weaker target gravity. Weight scales directly with this factor. Fall time scales in the opposite direction. Lower gravity gives longer fall time. It also gives higher jumps. The calculator maps jump height from source to target. It also predicts height from launch speed.
Practical Physics Uses
Use the tool for classroom demonstrations. Use it for planet design. Use it for game balancing. Use it for quick mission sketches. The output includes force, energy, pendulum timing, and impact speed. These results show how daily physics changes. A simple change in gravity affects many systems. The macro view keeps those changes organized. Always treat custom planets as estimates. Real planets can have uneven density. Local geology can also change gravity slightly. Still, the model gives a strong first calculation.
FAQs
1. What is a gravity transformation macro?
It is a scaling method that compares gravity on one body with gravity on another. It transforms weight, fall time, jump height, and other motion values.
2. Why does the calculator use effective gravity?
Effective gravity includes raw gravitational pull and the reduction caused by rotation. It better represents the gravity an object feels at a given latitude.
3. Can I use negative altitude?
Yes. Negative altitude is treated as depth. The calculator uses a simple uniform-density depth model, so it is an estimate, not a detailed geology model.
4. What does the transformation factor show?
It shows target effective gravity divided by source effective gravity. A value of 0.38 means the target gravity is 38 percent of the source gravity.
5. Why does latitude affect the answer?
Rotation reduces felt gravity most strongly near the equator. The correction becomes smaller toward the poles, so latitude changes the effective value.
6. Is this calculator useful for planets and moons?
Yes. You can compare planets, moons, asteroids, and custom bodies. Enter mass, radius, and rotation speed for the most relevant estimate.
7. Why is jump height higher in lower gravity?
The same launch speed fights less downward acceleration in lower gravity. That allows the object or person to rise higher before stopping.
8. Does this replace professional mission modeling?
No. It is a strong educational and planning calculator. Professional mission work needs detailed shape, density, terrain, atmosphere, and orbit models.