According to the theory of special relativity, an object moving at a high velocity relative to an observer will appear contracted in the direction of its motion. This phenomenon is known as length contraction or Lorentz contraction.
The length contraction effect is described by the Lorentz transformation, which relates the measurements of space and time between different frames of reference. According to this transformation, the length of an object as measured by an observer in a different frame of reference will appear shorter than its rest length (the length measured in the object's rest frame). The contraction factor, often denoted by γ (gamma), depends on the relative velocity between the observer and the object.
The contraction factor γ is given by the formula:
γ = 1 / sqrt(1 - v²/c²),
where v is the relative velocity between the observer and the object, and c is the speed of light. As the relative velocity approaches the speed of light (v → c), the contraction factor approaches infinity, meaning the length of the object appears to contract significantly.
So, in the scenario you mentioned, if an object with a rest length D is moving towards Earth at a velocity close to the speed of light, it will indeed appear contracted when observed from Earth. The observed length of the object will be shorter than D by a factor of γ, as predicted by special relativity.
It's important to note that length contraction is a relativistic effect that becomes noticeable at speeds approaching the speed of light. For everyday speeds, the contraction is negligible and not directly perceptible. Length contraction is one of the consequences of the spacetime geometry described by special relativity and has been experimentally verified in various experiments involving particle accelerators and high-speed particles.