No, that statement is not true. The claim that Archimedes would need a lever longer than the diameter of the observable universe to move the Earth using the moon as a pivot point is incorrect.
To understand why, let's consider some basic facts. Archimedes' principle states that with a lever, one can move a heavier object with less force by applying that force over a longer distance. However, even with an indestructible and unbending lever, there are fundamental physical limitations that make moving the Earth with human strength impossible.
The mass of the Earth is approximately 5.972 × 10^24 kilograms, and its average radius is about 6,371 kilometers. The distance between the Earth and the moon, on average, is approximately 384,400 kilometers. The moon's mass is about 7.348 × 10^22 kilograms.
For the sake of argument, let's assume Archimedes possesses superhuman strength capable of exerting a force equivalent to one million times the force of an average human. Even with such immense strength, it would be physically impossible for him to move the Earth using a lever, regardless of its length.
The length of the lever necessary to move the Earth would depend on the mechanical advantage required. To calculate this, we need to consider the torque, which is the force applied multiplied by the lever arm (distance from the pivot point). The torque required to move the Earth would be the product of the Earth's mass, its distance from the pivot point (moon), and the acceleration due to gravity.
Even with an unrealistically long lever, the torque exerted by Archimedes would still be insufficient to overcome the Earth's immense mass. The gravitational force between the Earth and the moon is much greater than any force Archimedes could exert, even with a hypothetical lever.
In conclusion, the claim that Archimedes would need a lever longer than the diameter of the observable universe to move the Earth with his strength using the moon as a pivot point is not accurate. The physical limitations of human strength and the massive scale of the Earth and moon make such an endeavor impossible, regardless of the lever's length.