Angle changes in Relativity (Shooting the Deathstar on a flyby)

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To determine the angle for shooting the Death Star while flying the Millennium Falcon at 0.8c, the equation cos(θ) = β is applied, yielding an angle of θ = 36.87°. This calculation suggests that as the speed (β) decreases, the angle approaches 90 degrees, which aligns with expectations in relativity. However, the user expresses concern that this problem seems overly simplistic compared to previous relativity challenges. Clarification on the complexity of the problem is sought, indicating a desire for deeper understanding of the relativity concepts involved.
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Homework Statement


You are flying the Millenium Falcon and want to shoot the Death Star at the closeest range possible. You fly by the Death star at speed .8c. Just at the time of your closest approach, the death star is 90° from your direction of motion, you shoot the laser gun at it. What is the angle you must set between your direction of motion and the laser gun?


Homework Equations



cos(θ)=β

The Attempt at a Solution



All I did was use the above equation and got that θ=36.87°, which would make sense because the smaller β is, the closer to 90 the angle would become. But this just seems way too easy compared to our other relativity problems, am I doing something wrong?

Thanks in advance!
 
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