Inverse-square gravity model
The calculator uses Newtonian gravitation to estimate the gravitational acceleration at radius r:
- G is the gravitational constant.
- M is the body mass.
- R is mean radius; h is altitude.
Escape speed and circular orbit speed use: vesc = √(2GM/r) and vorb = √(GM/r). The orbit period is T = 2πr / vorb.
Step-by-step
- Select a preset body (or check custom mode).
- Enter altitude above the surface in meters or kilometers.
- Provide a test mass to compute weight in newtons.
- Optional: set custom mass, radius, or adjust G.
- Press Submit to view results above the form.
- Use Download buttons for CSV or PDF reports.
Typical surface gravity values
Values below use preset mass and mean radius with the default gravitational constant.
| Body | Mass (kg) | Radius (m) | Surface g (m/s²) | Weight for 70 kg (N) |
|---|---|---|---|---|
| Mercury | 3.30110e+23 | 2.43970e+6 | 3.701618 | 259.113232 |
| Venus | 4.86750e+24 | 6.05180e+6 | 8.870387 | 620.927064 |
| Earth | 5.97219e+24 | 6.37100e+6 | 9.820286 | 687.42001 |
| Moon | 7.34200e+22 | 1.73740e+6 | 1.623381 | 113.636673 |
| Mars | 6.41710e+23 | 3.38950e+6 | 3.727977 | 260.958408 |
| Jupiter | 1.89820e+27 | 6.99110e+7 | 25.921293 | 1814.490523 |
| Saturn | 5.68340e+26 | 5.82320e+7 | 11.186405 | 783.048341 |
| Uranus | 8.68100e+25 | 2.53620e+7 | 9.007587 | 630.531116 |
| Neptune | 1.02413e+26 | 2.46220e+7 | 11.274938 | 789.245652 |
| Pluto | 1.30300e+22 | 1.18830e+6 | 0.615883 | 43.111783 |
Planetary gravity in practice
1) What gravity means for motion
Local gravity is the acceleration a freely falling object experiences (m/s²). It affects falling time, jump height, structural loads, and how strongly surfaces pull. On Earth, a common reference value is about 9.81 m/s².
2) Mass, radius, and the inverse-square rule
Newton’s model links gravity to the body’s mass and distance from its center through g = GM/r². If distance doubles, gravity becomes one quarter. If mass doubles, gravity doubles. Mean radius matters, so compact worlds can show strong surface gravity even without extreme total mass. For equal mass, a smaller radius boosts g sharply, so rocky super-Earths can feel heavy at the surface.
3) Why altitude reduces gravity
Altitude increases effective radius r = R + h, so g decreases. Near 400 km above Earth, gravity is still about 8.7 m/s² because r grows only ~6%. Astronauts feel weightless mainly because they are in continuous free fall.
4) Comparing common worlds
Surface gravity varies widely. The Moon is ~1.62 m/s², so 70 kg weighs ~113 N. Mars is ~3.7 m/s², near 260 N for 70 kg. Jupiter is ~24.8 m/s², about 1,740 N for 70 kg, illustrating how different environments change perceived heaviness.
5) Weight versus mass
Mass is an intrinsic property and stays constant. Weight is a force in newtons: W = m·g. The test-mass field converts your chosen mass into local weight using the computed g at the selected altitude.
6) Escape speed and orbit speed
Escape speed is the minimum speed to leave without further thrust. Circular orbit speed is lower because the craft keeps falling around the body. Both scale with GM/r, so denser or more massive bodies increase these speeds. They help compare how difficult it is to reach orbit or depart a world.
7) Orbit period and scale
Orbit period estimates the time for a circular path at your altitude. Higher orbits have larger radii and typically longer periods. Around Earth, many low orbits are roughly 1.5 hours, while higher orbits lengthen as radius grows. Geostationary altitude yields an approximate 24-hour period.
8) Using custom bodies responsibly
Custom mode helps with exoplanets, asteroids, or design studies. Use consistent units and sanity-check densities; tiny radii with huge masses imply extreme materials. Earth-mass and Earth-radius scaling can simplify inputs. For detailed work, include rotation, shape, and atmosphere beyond this ideal model.
Common questions
1) Why does gravity change with altitude?
Gravity depends on distance from the center. As altitude increases, r increases, and g falls as 1/r². The change is modest near the surface but becomes significant at very high altitudes.
2) Does “zero gravity” exist in orbit?
Gravity in low orbit is still strong. Astronauts feel weightless because they are in continuous free fall with their spacecraft, so there is no supporting force pushing back on them.
3) Which values should I use for mass and radius?
For planets, use total mass and mean radius. For small bodies, use the best available estimates. If the body is irregular, results are an average approximation, not a local field map.
4) What is the difference between g and weight?
g is acceleration (m/s²). Weight is force (newtons) computed as W = m·g. Your mass m stays constant, but your weight changes whenever g changes.
5) Why is the Earth comparison useful?
People have intuition for Earth gravity. The ratio g/g₀ shows how heavy or light things feel relative to Earth, making it easier to compare locations and interpret the results quickly.
6) Are these results exact for real planets?
No. The calculator uses an ideal spherical model. Real gravity varies with rotation, latitude, elevation, and internal structure. The values here are accurate enough for education and quick estimates.
7) When should I use custom G?
Most users should keep the default. Changing G is helpful for sensitivity checks or hypothetical physics. If you adjust it, remember all outputs that depend on g, orbit speed, and escape speed change.