An orbiting disco ball gave Einstein’s theory its most precise test yet
An orbiting disco ball gave Einstein’s theory its most precise test yet
一颗轨道上的“迪斯科球”为爱因斯坦的理论提供了迄今最精确的验证
Albert Einstein’s general theory of relativity predicts that a rotating mass like the Earth pulls the fabric of space and time around with it in a perpetual swirl. This phenomenon is known as frame dragging or the Lense-Thirring effect, after the two physicists who modeled it back in 1918. 阿尔伯特·爱因斯坦的广义相对论预言，像地球这样旋转的质量体会带动周围的时空结构一起旋转。这种现象被称为“参考系拖拽”（frame dragging）或“兰斯-蒂林效应”（Lense-Thirring effect），以1918年对其进行建模的两位物理学家的名字命名。
Frame dragging becomes more significant with larger masses and faster rotation, so we’ve mainly observed it around huge black holes. Measuring how much the Earth twists spacetime as it rotates has been much more challenging because our pale blue dot of a planet is millions of times lighter than a typical black hole and rotates rather slowly. 参考系拖拽效应在质量更大、旋转速度更快的物体周围表现得更为显著，因此我们主要是在巨大的黑洞周围观测到它。测量地球在自转时对时空的扭曲程度要困难得多，因为我们这颗“暗淡蓝点”行星的质量比典型的黑洞轻数百万倍，且自转速度相当缓慢。
But now, a team of astronomers led by Ignazio Ciufolini, a physicist at the Wuhan Institute of Physics and Mathematics in China, reports the most accurate measurement of the terrestrial Lense-Thirring effect to date. Their work brings our uncertainty down from a few percentage points to just 0.2 percent. And they did it with a satellite that looks like a cross between a golf ball and a disco globe. 但现在，由中国武汉物理与数学研究所的物理学家伊格纳齐奥·丘福里尼（Ignazio Ciufolini）领导的天文学家团队报告了迄今为止对地球兰斯-蒂林效应最精确的测量结果。他们的研究将不确定性从几个百分点降低到了仅0.2%。而他们实现这一目标所使用的卫星，看起来就像是高尔夫球和迪斯科球的结合体。
Disco globe satellite
迪斯科球卫星
The disco globe satellite that Ciufolini and his colleagues use in their experiment is called LARES-2 (Laser Relativity Satellite 2) and has been developed by the Italian Space Agency. It’s a solid sphere of Inconel 718, a dense nickel-chromium alloy, covered with 303 corner-cube retroreflectors and measuring a bit over 40 centimeters across. It has no thrusters, no solar panels, and no electronics of any kind. It weighs 294.8 kilos. 丘福里尼及其同事在实验中使用的这颗迪斯科球卫星被称为LARES-2（激光相对论卫星2号），由意大利航天局开发。它是一个由因科内尔718合金（一种致密的镍铬合金）制成的实心球体，表面覆盖着303个角锥棱镜反射器，直径略超过40厘米。它没有推进器，没有太阳能电池板，也没有任何电子设备，重达294.8公斤。
That combination of small size and large mass gives it the lowest area-to-mass ratio of any satellite in medium-Earth orbit. This was exactly what the scientists needed, since it helped them minimize the impact of other forces. 这种小尺寸与大质量的结合，使其成为中地球轨道上所有卫星中面积质量比最低的一颗。这正是科学家们所需要的，因为它有助于最大限度地减少其他力的影响。
“The idea is that we want to measure gravitation,” Ciufolini said. “We have non-gravitational effects like photons impinging on the satellite and pushing it. So, the mass must be very large and the cross-section of the satellite very small, so the acceleration induced by photons is very, very small.” “我们的初衷是测量引力，”丘福里尼说，“我们面临着非引力效应，比如光子撞击卫星并对其产生的推力。因此，卫星的质量必须非常大，横截面积必须非常小，这样光子引起的加速度才会非常、非常小。”
In theoretical physics, satellites of this kind are called test particles, meaning an object whose motion is governed almost entirely by the gravitational field. LARES-2 was placed in orbit at an altitude of roughly 12,265 kilometers by a Vega-C rocket in July 2022. Once the LARES-2 was in position, the researchers started shooting it with ground-based lasers. 在理论物理学中，这类卫星被称为“测试粒子”，意味着其运动几乎完全受引力场支配。2022年7月，LARES-2由织女星-C（Vega-C）火箭送入约12,265公里的轨道。一旦LARES-2进入预定位置，研究人员就开始用地面激光对其进行照射。
Synchronous flying
同步飞行
The retroreflectors on LARES-2 are designed to reflect a beam of light exactly in the direction this beam came from. When Ciufolini and his colleagues fired short laser pulses at the satellite, they could pinpoint its position down to roughly 1 millimeter based on the light that came back. About 200,000 such observations, spanning July 2022 to June 2025, formed the dataset the team used to measure Earth’s frame dragging. LARES-2上的反射器旨在将光束精确地反射回光源方向。当丘福里尼及其同事向卫星发射短激光脉冲时，他们可以根据反射回来的光线将其位置精确到约1毫米。从2022年7月到2025年6月，约20万次此类观测构成了团队测量地球参考系拖拽效应的数据集。
But even such precise positioning was not enough to achieve the accuracy the team wanted. The problem with measuring frame dragging using Earth-orbiting satellites is that the Earth is not a perfect sphere. Its equatorial bulge produces classical Newtonian forces on satellite orbits that are orders of magnitude larger than the frame dragging signal. 但即使是如此精确的定位，也不足以达到团队想要的精度。利用地球轨道卫星测量参考系拖拽的问题在于，地球并非一个完美的球体。其赤道隆起对卫星轨道产生的经典牛顿力，比参考系拖拽信号大几个数量级。
The solution Ciufolini proposed decades ago while working with physicist John Archibald Wheeler was to use two satellites in supplementary orbits, meaning with orbital inclinations that sum to 180 degrees. 丘福里尼几十年前与物理学家约翰·阿奇博尔德·惠勒（John Archibald Wheeler）合作时提出的解决方案是：使用两颗处于互补轨道上的卫星，即它们的轨道倾角之和为180度。
“Suppose we have a satellite orbiting around a perfectly spherically symmetric object—the orbit of this satellite would act like a gyroscope,” Ciufolini said. Under ideal conditions, the orbital plane and its orientation in space would remain fixed, and the only thing altering this orientation should be frame dragging. “假设我们有一颗绕着一个完美球对称物体运行的卫星，这颗卫星的轨道就像一个陀螺仪，”丘福里尼说。在理想条件下，轨道平面及其在空间中的取向将保持固定，唯一能改变这种取向的因素应该是参考系拖拽。
“But the Earth is not spherically symmetric,” Ciufolini said. “It is oblate, and this oblateness produces a change in the orientation of the orbital plane.” With two satellites at supplementary inclinations, the Newtonian perturbations are equal and opposite in the two orbital planes and cancel each other out. The Lense-Thirring effect, which pushes both orbital planes in the same direction, adds algebraically—the noise vanishes and the relativistic signal survives. “但地球不是球对称的，”丘福里尼说，“它是扁圆的，这种扁率会导致轨道平面的取向发生变化。”通过两颗处于互补倾角的卫星，牛顿摄动在两个轨道平面上大小相等、方向相反，从而相互抵消。而将两个轨道平面向同一方向推动的兰斯-蒂林效应则会代数相加——噪声消失，相对论信号得以保留。
That’s why LARES-2 was working in synchrony with its older and larger cousin called LAGEOS, a NASA satellite designed exclusively for high-precision laser-ranging, launched in 1976. The orbital inclinations LAGEOS and LARES-2 summed up to 180.01 degrees, which the team considered close enough. But the Earth’s irregular shape was not the only challenge. 这就是为什么LARES-2要与其更古老、更大的“表亲”LAGEOS协同工作的原因。LAGEOS是NASA一颗专门用于高精度激光测距的卫星，于1976年发射。LAGEOS和LARES-2的轨道倾角之和为180.01度，团队认为这已经足够接近了。但地球的不规则形状并不是唯一的挑战。
Fighting the tide
对抗潮汐
With the Newtonian noise solved by clever geometric cancellation, one remaining perturbation to deal with was something called the K1 lunisolar tide, a gravitational disturbance from the Moon and Sun that modulates Earth’s gravitational field. 随着牛顿噪声通过巧妙的几何抵消得到解决，剩下的一个需要处理的摄动是所谓的“K1日月潮汐”，这是一种来自月球和太阳的引力扰动，会调节地球的引力场。
“The Sun and the Moon change the shape of the Earth, and the shape of the Earth changes the gravitational field around it, which changes the orbit of the satellite a little bit,” Ciufolini said. “The main challenge of this experiment was to get rid of this one tide.” “太阳和月球改变了地球的形状，而地球形状的改变又改变了其周围的引力场，进而轻微改变了卫星的轨道，”丘福里尼说，“这项实验的主要挑战就是消除这种潮汐影响。”
The team’s solution was to collect measurements from exactly one complete 1,050-day precession cycle of the satellites. Over that period, the tidal perturbation, with well-measured period and phase, averages out and can be removed from the data. 团队的解决方案是收集卫星正好一个完整的1,050天进动周期的数据。在此期间，具有明确测量周期和相位的潮汐摄动会相互抵消，从而可以从数据中剔除。
After removing the tidal signal and six smaller tidal components with known periods between 135 and 910 days, the researchers were left with a clean, steady drift in the satellites’ combined orbits of about 61.3 milliarcseconds per year—the signature of spacetime twisting. This final measured value came in incredibly close to Einstein’s general relativity predictions, carrying a tiny margin of error of just one to two parts per thousand based on their statistical models. 在剔除了潮汐信号以及六个周期在135到910天之间的较小潮汐分量后，研究人员得到了卫星组合轨道上每年约61.3毫角秒的清晰、稳定的漂移——这就是时空扭曲的特征。这一最终测量值与爱因斯坦广义相对论的预言极其吻合，基于其统计模型，误差范围仅为千分之一到千分之二。
Post-Einstein physics
后爱因斯坦物理学
The measurement confirmed general relativity… 该测量结果证实了广义相对论……