📚 Gravitational Field Strength g / N kg⁻¹ | 重力场强度 g / 牛每千克
In AQA A-level Physics, the symbol g is used for gravitational field strength. It may be quoted in newtons per kilogram, N kg⁻¹, or equivalently in metres per second squared, m s⁻². This article explains what g means, how the unit arises, how g behaves in uniform and radial fields, and how it is measured in the laboratory.
在 AQA A-level 物理中，符号 g 表示重力场强度。它可以用牛每千克（N kg⁻¹）表示，也可以等效地用米每二次方秒（m s⁻²）表示。本文将解释 g 的含义、单位的来源、g 在均匀场和径向场中的表现，以及如何在实验中测量 g。
1. What is gravitational field strength? | 什么是重力场强度？
Gravitational field strength at a point is defined as the gravitational force per unit mass acting on a small test mass placed at that point. It is a vector quantity, so it has both magnitude and direction. The direction of g is the direction of the gravitational force on a test mass, which is toward the centre of the source mass.
重力场强度在某点定义为单位质量的小试探质量在该点所受的重力。它是矢量，既有大小又有方向。g 的方向是作用在试探质量上的重力方向，总是指向源质量的中心。
itational force in newtons and m is the test mass in kilograms. This definition immediately gives the SI unit N kg⁻¹. The field strength does not depend on the test mass itself for a given field.
用符号表示：g = F / m，其中 F 是重力（单位牛），m 是试探质量（单位千克）。这个定义直接给出了 SI 单位 N kg⁻¹。对于给定的场，场强与试探质量本身无关。
2. Why the unit is N kg⁻¹ | 为什么单位是 N kg⁻¹
The unit comes from dividing force by mass. Since force is measured in newtons and mass in kilograms, gravitational field strength has the unit N kg⁻¹. One newton per kilogram means that a 1 kg mass experiences a gravitational force of 1 N at that point.
这个单位来自力除以质量。因为力的单位是牛，质量的单位是千克，所以重力场强度的单位是 N kg⁻¹。1 N kg⁻¹ 表示在该点 1 kg 的质量受到 1 N 的重力。
emphasises the field concept, while m s⁻² emphasises acceleration in a free-fall context.
该单位在量纲上等同于 m s⁻²，因为 1 N = 1 kg m s⁻²。因此 1 N kg⁻¹ = 1 m s⁻²。不过，N kg⁻¹ 强调场的概念，而 m s⁻² 强调自由落体中的加速度。
| Quantity | Unit | Equivalent form |
|---|---|---|
| g = F / m | N kg⁻¹ | m s⁻² |
3. g as force per unit mass | g 作为单位质量所受的力
A gravitational field is a region of space where a mass experiences a non-contact force. The field strength g tells us how strong that field is at a point, independent of the mass of the object placed there, provided the object is small enough not to disturb the source field significantly.
重力场是空间中质量受到非接触力的区域。场强 g 表示该点场的强弱，与放在那里的物体质量无关，只要物体足够小、不显著干扰源场即可。
emains 9.81 N kg⁻¹ whether the mass is 1.0 kg or 10.0 kg, because g is a property of the field, not the object.
对于测试质量 m，重量为 W = mg。在地球上，2.0 kg 的物体重量为 W = 2.0 × 9.81 = 19.6 N。无论质量是 1.0 kg 还是 10.0 kg，场强始终为 9.81 N kg⁻¹，因为 g 是场的属性，而不是物体的属性。
4. Uniform and radial fields | 均匀场与径向场
rection at all points. The field lines are parallel and equally spaced. Close to the Earth' ace, the field is approximately uniform with g ≈ 9.81 N kg⁻¹ directed vertically downward.
在均匀重力场中，g 的大小和方向在所有点都相同。场线平行且等距。接近地球表面时，场近似均匀，g ≈ 9.81 N kg⁻¹，方向竖直向下。
In a radial field, such as the field around a planet or star, field lines point radially inward toward the centre of mass. The magnitude of g decreases with distance from the centre according to an inverse-square law, so field lines spread out as distance increases.
在径向场中，例如行星或恒星周围的场，场线沿径向指向质心。g 的大小随距中心的距离按平方反比定律减小，因此随着距离增大，场线会散开。
5. Newton's law and g = GM / r² | 牛顿定律与 g = GM / r²
Newton' is the test mass, r is the distance between their centres, and G = 6.67 × 10⁻¹¹ N m² kg⁻².
牛顿万有引力定律给出两个点质量之间的力：F = GMm / r²，其中 M 是源质量，m 是测试质量，r 是它们中心之间的距离，G = 6.67 × 10⁻¹¹ N m² kg⁻²。
This shows that g depends only on the source mass M and the distance r, not on the test mass. For a spherical body such as a planet, the same formula applies outside the body if r is measured from its centre.
除以测试质量 m 得到径向场强：g = F / m = GM / r²。这说明 g 只取决于源质量 M 和距离 r，而与测试质量无关。对于行星这样的球体，只要 r 从其中心量起，同一公式在球体外部同样适用。
g = GM / r²
6. g near the Earth's surface | 地球表面附近的 g
At the Earth's surface, r is approximately the Earth' g ≈ 9.81 N kg⁻¹. This is the average surface field strength used in most AQA calculations.
在地球表面，r 约为地球半径 R = 6.37 × 10⁶ m，M = 5.97 × 10²⁴ kg。代入 g = GM / r² 可得到 g ≈ 9.81 N kg⁻¹。这是大多数 AQA 计算中使用的平均表面场强。
The actual value of g at the surface varies from about 9.78 N kg⁻¹ at the equator to 9.83 N kg⁻¹ at the poles, due to Earth's rotation and its oblate shape. These variations are small but measurable with precise instruments.
地表实际的 g 值从赤道约 9.78 N kg⁻¹ 到两极约 9.83 N kg⁻¹ 不等，原因是地球自转及其扁球形状。这些变化很小，但可以用精密仪器测量出来。
7. Variation of g with height and latitude | g 随高度和纬度的变化
For a point above the Earth' is Δg ≈ -2GMh / R³, so moving upward by a few metres produces only a tiny reduction in g.
在地球表面上方高度 h 处，场强为 g = GM / (R + h)²。随着 h 增大，g 减小。对于小高度，近似变化为 Δg ≈ -2GMh / R³，因此向上移动几米只会使 g 产生极小的减小。
Latitude also affects g. The Earth bulges at the equator, so the equatorial radius is larger, reducing g. In addition, the centripetal effect of Earth's rotation reduces the measured g at the equator compared with the poles.
纬度也会影响 g。地球在赤道处隆起，因此赤道半径较大，使 g 减小。此外，地球自转的向心效应使赤道处测得的 g 小于两极。
| Location | g / N kg⁻¹ |
|---|---|
| Earth surface average | 9.81 |
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