If an observer on Earth were to observe a spaceship moving at a significant fraction of the speed of light, they would indeed perceive certain effects due to time dilation and length contraction. Let's consider a scenario where the spaceship is moving relative to Earth at a very high velocity:
Time dilation: According to the theory of relativity, time dilation occurs when objects move at high speeds relative to each other. From the perspective of the observer on Earth, they would perceive time running slower for the spaceship relative to their own time. This means that the clocks on the spaceship would appear to be ticking slower compared to the clocks on Earth. Therefore, the observer on Earth would see the spaceship's internal processes and the movement of its occupants as slowed down.
Length contraction: Another effect to consider is length contraction. As an object moves at high velocities, its length in the direction of motion appears to contract from the perspective of a stationary observer. Therefore, the observer on Earth would see the spaceship appearing shorter in the direction of its motion compared to its rest length.
Doppler effect: Additionally, the observer on Earth would perceive a Doppler effect due to the relative motion between the spaceship and Earth. If the spaceship is moving towards Earth, the observer would see the light emitted from the spaceship being blueshifted (shifted towards shorter wavelengths), making it appear more energetic. Conversely, if the spaceship is moving away from Earth, the observer would see the light being redshifted (shifted towards longer wavelengths), making it appear less energetic.
It's important to note that these effects become more pronounced as the spaceship approaches the speed of light. At speeds that are a significant fraction of the speed of light, time dilation and length contraction can become substantial, resulting in noticeable differences in how the spaceship is observed from Earth.
However, it's worth mentioning that from the perspective of the occupants on the spaceship, they would experience time passing at a normal rate within their frame of reference. It would be the observers on Earth who perceive the time dilation and length contraction effects due to the relative motion between the spaceship and Earth.
These relativistic effects have been confirmed by experimental evidence and are an integral part of our understanding of how the universe works at high speeds and in gravitational fields.