📚 Gravitational Fields | 引力场
Gravitational fields are a fundamental concept in physics that describe the region of space surrounding a mass where another mass experiences an attractive force. In this article, we explore Newton's law of gravitation, field strength, potential, orbital mechanics, and the energy considerations that underpin satellite motion and escape velocities, closely following the CIE A-Level syllabus.
引力场是物理学中的一个基本概念，描述了质量周围空间中另一质量受到吸引力的区域。本文依据 CIE A-Level 教学大纲，探讨牛顿万有引力定律、场强、势能、轨道力学以及能量考量，这些是卫星运动和逃逸速度的基础。
1. Newton’s Law of Gravitation | 牛顿万有引力定律
Newton's law of universal gravitation states that every point mass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
牛顿万有引力定律指出，每个质点都会吸引其他质点，引力的大小与两质点质量的乘积成正比，与它们中心之间距离的平方成反比。
The force can be expressed as F = G m₁ m₂ / r² ional constant, 6.67 × 10⁻¹¹ N m² kg⁻², m₁ and m₂ are the masses, and r is the separation.
该力可表示为 F = G m₁ m₂ / r²，其中 G 为引力常数 6.67 × 10⁻¹¹ N m² kg⁻²，m₁ 与 m₂ 为两质量，r 为间距。
The force is always attractive, acts along the line joining the centres, and obeys Newton's third law (the forces on the two masses are equal and opposite).
引力总是吸引力，沿两中心连线作用，并遵循牛顿第三定律（两质量所受的力大小相等、方向相反）。
2. Gravitational Field Strength | 引力场强度
Gravitational field strength g at a point is defined as the gravitational force per unit mass experienced by a small test mass placed at that point: g = F / m.
引力场强度 g 在某点的定义为放置在该点的小测试质量所受到的每单位质量的引力：g = F / m。
For a point mass (or outside a uniform sphere), the magnitude of g is given by g = G M / r², directed radially towards the centre of the mass M.
对于质点（或均匀球体外部），g 的大小为 g = G M / r²，方向沿径向指向质量 M 的中心。
Near the Earth’s surface, the field is approximately uniform with g ≈ 9.81 N kg⁻¹ (or m s⁻²). This is a special case where r is approximately the Earth’s radius.
靠近地球表面处，引力场近似为均匀场，g ≈ 9.81 N kg⁻¹（或 m s⁻²）。这是 r 约等于地球半径的特殊情况。
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 without acceleration. It is given by V = - G M / r, with the zero of potential defined at infinity.
引力势 V 在某点是指将单位小质量从无穷远处匀速移至该点所做的功。其表达式为 V = - G M / r，零势点取在无穷远。
The negative sign indicates that gravity does negative work (the field does work) as a mass is brought from infinity; work must be done against the gravitational attraction to move a mass away.
负号表明，当质量从无穷远移来时引力做负功（场做正功）；要使质量远离，需要克服引力做功。
Potential is a scalar quantity and is measured in J kg⁻¹. The potential gradient is related to the field strength by g = - dV/dr for a radial field.
势能是标量，单位为 J kg⁻¹。对于径向场，势能梯度与场强的关系为 g = - dV/dr。
4. Gravitational Potential Energy | 引力势能
The gravitational potential energy U of a system of two point masses is the energy required to separate them to infinity from a distance r. It is given by U = - G M m / r.
由两个质点组成的系统的引力势能 U 是指将它们从距离 r 分离至无穷远所需的能量，表达式为 U = - G M m / r。
U is negative because the masses are in a bound state; work must be done against the gravitational field to increase separation. For a mass m in the field of M, U = m V.
U 为负值是因为两质量处于束缚态；必须克服引力场做功才能增加间距。对于位于
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