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Relativity is a fundamental concept in physics that was revolutionized by Albert Einstein's Theory of Relativity. It essentially describes how the laws of physics are the same for all non-accelerating observers, and it introduces the idea that space and time are interwoven into a single continuum known as spacetime.
One of the key ideas in relativity is that the speed of light is constant for all observers, regardless of their motion relative to the light source. This leads to several surprising effects, such as time dilation and length contraction. In particular, when objects move at speeds close to the speed of light, their observed behavior changes significantly from what we would expect in classical mechanics.
In the problem involving the spaceship, relativity comes into play because the spaceship is traveling at a significant fraction of the speed of light (0.90c). This high speed means we must use the principles of relativity, rather than classical physics, to accurately describe how the pulses of light are perceived on Earth.

Light pulses in the realm of physics refer to brief bursts of light emitted from a source. These pulses can be used to transmit information or to perform various measurements. Because light is composed of photons, these pulses essentially consist of numerous photons moving through space.
A critical aspect of light is its electromagnetic nature, which means it can travel through a vacuum and its speed is the universal speed limit, noted as "c." The speed of light in a vacuum is approximately 299,792,458 meters per second. In this context, the light source on the spaceship emits an impressive number of pulses each second, specifically, \(2 \times 10^{15}\) pulses, while moving almost as fast as light itself.
Understanding how these light pulses travel and are perceived is crucial when looking at scenarios involving high velocities, such as those described by special relativity. When the spaceship travels at such high speeds compared to the stationary observer on Earth, peculiar effects on the light pulses, due to relativistic principles, must be taken into account.

Frequency calculation in physics involves determining the rate at which waves repeat over a specific time period. It is often expressed in Hertz (Hz), indicating cycles per second. In this exercise, frequency calculation deals with determining how many light pulses are observed on Earth each second, given the relativistic effects at play.
Due to the transverse Doppler effect, the observed frequency of light changes when the source is moving relative to the observer. This effect considers not the path of travel directly towards or away from the observer, but perpendicular to the travel direction, as is the case here. The formula used for this frequency shift is:
\[ f = f_0 \sqrt{1 - \frac{v^2}{c^2}} \]
where \( f \) is the frequency observed on Earth, \( f_0 \) is the rest frame frequency (\(2 \times 10^{15} \) pulses/sec), \( v \) is the velocity of the spaceship, and \( c \) is the speed of light.
By substituting the given values into the formula, we calculate the observed frequency as \( 8.7 \times 10^{14} \) pulses each second. This reduction in observed frequency illustrates how relativistic speeds affect the perception of time and frequency, fundamental to understanding the finer points of relativity and its implications.