引力计算器
本引力计算器使用牛顿万有引力定律 F = G × m₁ × m₂ / r² 计算任意两个质量之间的吸引力。选择未知变量，输入三个已知值，即时得出结果——包括地球-太阳、地球-月球或任意自定义系统。
G = 6.674e-11 N·m²/kg² (gravitational constant)
常见问题
如何计算两个物体之间的引力？
根据牛顿万有引力定律，引力 F = G × m₁ × m₂ / r²，其中 G = 6.674 × 10⁻¹¹ N·m²/kg² 是引力常数，m₁ 和 m₂ 是两个物体的质量，r 是它们之间的距离。
什么是引力常数 G？
引力常数 G = 6.674 × 10⁻¹¹ N·m²/kg²，由英国物理学家卡文迪许（Henry Cavendish）于 1798 年首次精确测量。G 是自然界最难精确测量的基本物理常数之一。
引力与距离的关系是什么？
引力与距离的平方成反比（平方反比定律）。距离加倍，引力减少为原来的 1/4；距离缩短为一半，引力增加为原来的 4 倍。这就是为什么离地球越远，重力越弱。
引力和重力有什么区别？
引力是任意两个有质量的物体之间的普遍吸引力；重力特指地球对地面物体的引力，等于 mg（m 为质量，g = 9.8 m/s²）。重力是引力的特例，g 值是地球表面引力加速度的近似值。
Newton's Law of Universal Gravitation
Every object with mass attracts every other object with mass. Newton's law of universal gravitation quantifies this attraction as a function of the two masses and the distance between them.
Formula
F = G × m₁ × m₂ / r²
Variables
- F — gravitational force (Newtons, N)
- G — gravitational constant: 6.674 × 10⁻¹¹ N·m²/kg²
- m₁ — mass of object 1 (kilograms, kg)
- m₂ — mass of object 2 (kilograms, kg)
- r — distance between the centers of the two masses (meters, m)
How to Use This Calculator
Select the variable you want to calculate, then fill in the other three fields. The calculator solves for the unknown in real time.
Example: Earth–Sun Force
- m₁ (Earth) = 5.97 × 10²⁴ kg
- m₂ (Sun) = 1.989 × 10³⁰ kg
- r = 1.496 × 10¹¹ m (1 AU)
- F ≈ 3.54 × 10²² N
Derived Formulas
| Solve For | Formula |
|---|---|
| Force (F) | F = G × m₁ × m₂ / r² |
| Mass 1 (m₁) | m₁ = F × r² / (G × m₂) |
| Mass 2 (m₂) | m₂ = F × r² / (G × m₁) |
| Distance (r) | r = √(G × m₁ × m₂ / F) |
Common Gravitational Forces
| System | Force (N) |
|---|---|
| Earth–Moon | 1.98 × 10²⁰ |
| Earth–Sun | 3.54 × 10²² |
| Two 1 kg balls, 1 m apart | 6.67 × 10⁻¹¹ |
| Person (70 kg) on Earth surface | 686 (≈ weight) |
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