How do scientists measure and observe Earth's rotation to confirm it matches classical mechanics theories?

 Earth spins at 1,000 mph, yet to measure its exact rotation, scientists must track supermassive black holes billions of light-years away.

But the first undeniable, direct observation of Earth's rotation came much closer to home in 1851, courtesy of French physicist Léon Foucault. He suspended a 62-pound brass-coated lead bob from the dome of the Panthéon in Paris using a 220-foot wire. Once set in motion, the pendulum swung back and forth, but over the course of the day, the path of its swing slowly rotated clockwise. Classical mechanics dictates that a freely swinging pendulum will maintain its plane of oscillation unless acted upon by an outside force. The pendulum was not actually rotating; the building, and the Earth attached to it, was rotating beneath it. This elegantly demonstrated the Coriolis effect and proved the planet's rotation without the need to look at the sky.

Today, observing Earth's rotation requires far more precision. The planet does not spin perfectly smoothly; its rotation is constantly nudged by ocean tides, atmospheric winds, and shifting magma in the core. To measure these microscopic variations in the length of a day, scientists rely on advanced techniques:

• Very Long Baseline Interferometry (VLBI): A global network of radio telescopes points at quasars—supermassive black holes emitting massive amounts of energy billions of light-years away. Because they are so incredibly distant, quasars appear completely stationary, acting as perfect fixed reference points. By measuring the microscopic time differences in when a radio signal from a quasar reaches different telescopes around the globe, scientists can calculate Earth's exact orientation and rotation rate down to the millimeter.
• Ring Laser Gyroscopes: To measure rotation directly from the ground without astronomical references, scientists use massive optical interferometers, like the "G" ring laser in Germany. Deep underground, a laser beam is split and sent in opposite directions around a closed square loop. Because the Earth is spinning, the beam traveling with the rotation takes slightly longer to complete the circuit than the beam traveling against it. This phenomenon, known as the Sagnac effect, produces an interference pattern that reveals minute changes in Earth's spin on a daily basis.

By combining 19th-century mechanical principles with modern optical and radio astronomy, researchers continually confirm that classical mechanics flawlessly describe a planet that is constantly wobbling, slowing down, and speeding up in the dark.

How do scientists measure and track something as far away as Voyager 1 in space?

 Great question!

Since the signals from the two Voyager spacecraft are SO faint at their current distances (e.g., Voyager 1 is an entire light-day from Earth), if we did not have a very good idea where they are, we would be unlikely to ever find them.

As to the instruments used to communicate with them, we rely on the NASA Deep Space Network, supplemented occasionally by the Very Large Array, the Very Long Baseline Array, the European Deep Space Network and the Japanese Deep Space Network.

Here is a rough diagram of the NASA DSN:

and here are pictures of the radiotelescopes at each location:

We are currently in the process of upgrading the dishes at each location: