# Incoming!

A spacecraft approaching Earth very quickly is observed at a distance of $$D.$$ This has never happened before, so you check your instruments for time $$\Delta t,$$ and then you check the position of the craft again.

Now you can see it at a distance of $$D- 3 c \Delta t,$$ where $$c$$ is the speed of light.

The craft is traveling at a constant speed of $$v$$ directly toward Earth. What is $$v?$$

Assume you have made your measurements from an inertial frame very close to Earth.


Hint: The correct solution requires no transformation.

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