📚 Gravitational Fields and Satellites | 引力场与卫星
Gravitational fields describe the influence that a mass exerts on the space around it, allowing it to attract other masses without contact. In International A-level Physics, this topic connects Newton's law of gravitation, field strength, potential, orbital motion and satellite applications. Understanding these ideas is essential for solving problems on planetary motion and satellite technology.
引力场描述质量对其周围空间产生的影响，使它能够在没有接触的情况下吸引其他质量。在国际A-level物理中，本主题将牛顿万有引力定律、场强、引力势、轨道运动和卫星应用联系起来。理解这些概念对于解决行星运动和卫星技术问题至关重要。
1. Newton's Law of Gravitation | 牛顿万有引力定律
Newton's law of gravitation states that any two point masses attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of their separation.
牛顿万有引力定律指出，任何两个质点都会相互吸引，引力的大小与两质量的乘积成正比，与它们之间距离的平方成反比。
F = Gm₁m₂ / r²
he force acts along the line joining the two centres of mass and is always attractive. This law applies exactly to point masses and also to spherical masses when r is measured from their centres.
其中 G 是万有引力常量，G = 6.67 × 10⁻¹¹ N m² kg⁻²。引力沿两个质心连线方向作用，并且始终是吸引力。该定律精确适用于质点，也适用于球形质量，此时 r 从两球心之间测量。
2. Gravitational Field Strength | 引力场强度
test mass placed at a point: g = F / m. Its unit is N kg⁻¹, which is equivalent to m s⁻².
引力场强度 g 定义为放置在该点的小检验质量所受到的每单位质量的引力：g = F / m。其单位是 N kg⁻¹，等价于 m s⁻²。
In a radial field around a point mass or spherical mass M, the field strength at distance r from the centre is:
在点质量或球形质量 M 周围的径向场中，距中心 r 处的场强为：
g = GM / r²
hows an inverse-square law: doubling the distance reduces g to one quarter. Near the Earth' eld lines point radially inwards towards the mass, and their spacing shows field strength.
这表明平方反比定律：距离加倍会使 g 减小到原来的四分之一。在地球表面附近，引力场近似均匀，g ≈ 9.81 N kg⁻¹。场线沿径向指向质量，场线的疏密表示场强大小。
3. Gravitational Potential | 引力势
Gravitational potential V at a point is the work done per unit mass in bringing a small test mass from infinity to that point. Since gravity does positive work as a mass moves from infinity, V is negative in a gravitational field.
引力势 V 是单位质量从无穷远移动到该点所做的功。由于质量从无穷远移入时引力做正功，因此引力场中的 V 为负值。
V = -GM / r
V is a scalar quantity measured in J kg⁻¹. At infinite separation, V is defined as zero. Unlike gravitational field strength, potential can be added algebraically when several masses are present.
V 是
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