Library / Foundations: Physics / FPH-26
Foundations: Physics
Gravitational field and orbit
Field strength at a distance from a spherical mass.
- Ref
- FPH-26
- Rev
- v1
- Field
- Foundations: Physics
- Result
- g [N/kg]
Outside a spherical mass M, measure r from its centre. Potential is zero at infinity. The field points towards M. G = 6.674×10⁻¹¹ N m² kg⁻².
Gravity weakens with the square of the distance from the centre of the planet.
Calculator
- Orbital speed √(GM/r)7.91 km/s
- Potential −GM/r−62.56 MJ/kg
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Orbital speed falls with distance, so low orbits are fast.
- At the surface of a planet this gives the familiar weight per kg.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (N/kg) | Local step | Change in result |
|---|---|---|---|---|---|---|
| M Mass | 0.07 to 2,000 10²⁴ kg | 0.1151 | 3,289 | 3,289 | +10% | +10 % |
| r Distance from centre | 1.7 to 100 10⁶ m | 0.03986 | 137.9 | 137.9 | +10% | −17.4 % |
Sweep of Distance from centre
| Distance from centre (10⁶ m) | Field strength (N/kg) |
|---|---|
| 1.7 | 137.9 |
| 2.829 | 49.8 |
| 4.708 | 17.98 |
| 7.835 | 6.493 |
| 13.04 | 2.345 |
| 21.7 | 0.8466 |
| 36.11 | 0.3057 |
| 60.09 | 0.1104 |
| 100 | 0.03986 |
Sweep one variable
Variables and how each one contributes
Field strength
What the equation gives you. Everything else feeds it.
Mass
Mass of the body (Earth 5.972). Directly proportional.
Distance from centre
Distance from the centre (Earth radius 6.371). Inverse square: doubling the distance cuts the field to a quarter.
Worked example with the values above
- GM = 6.674×10⁻¹¹ × 5.972×10²⁴ = 3.986×1014 m³/s².
- r² = (6.371×10⁶)² = 4.059×1013 m².
- g = 9.82 N/kg.
Assumptions and limits
- Spherical, non-rotating body.
- Point at or above the surface.
Common mistakes
- Measuring r from the surface instead of the centre.
- Mixing 10⁶ m with km.
Statistics and uncertainty
G is known to only about 5 significant figures, so it limits precision more than most other inputs.
Where it is used
- Satellite and orbit calculations.
- Surface gravity on other bodies.
Maths you need
- Inverse square law: 1/r²
- Scientific notation: powers of ten