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ধরা যাক, NASA পৃথিবী থেকে 200 আলোকবর্ষ দূরের একটি সৌরজগৎ 🌍🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀
এই পৃষ্ঠায়, NASA ২০ বছর আলোকবর্ষ দূরের একটি নক্ষত্রজগতে ভ্রমণকালে মহাকাশচারী নভোযানের ভেতরের সময় কতটুকু অতিবাহিত হবে, তা গণনা করার জন্য, প্রথমে প্রদত্ত:
যেহেতু মহাকাশযান আলোর গতির কাছাকাছি গতিতে ভ্রমণ করছে, তাই এখানে সময়ের আপেক্ষিকতার ধারণা প্রযোজ্য হবে। মহাকাশযানের নিজস্ব কাঠামোতে (frame of reference) অতিবাহিত সময় পৃথিবীর পর্যবেক্ষকের তুলনায় কম হবে। এই প্রভাবকে সময় dilation বা কাল দীর্ঘায়ন বলা হয়।
কাল দীর্ঘায়নের সূত্রটি হল:
\[ t' = \frac{t}{\gamma} \] যেখানে:১. লরেন্টজ গুণক \( \gamma \) নির্ণয়:
\[ \gamma = \frac{1}{\sqrt{1 - \frac{(0.99c)^2}{c^2}}} = \frac{1}{\sqrt{1 - 0.99^2}} = \frac{1}{\sqrt{1 - 0.9801}} = \frac{1}{\sqrt{0.0199}} \approx 7.088 \]২. পৃথিবীর কাঠামোতে অতিবাহিত সময় \( t \) নির্ণয়:
পৃথিবীর কাঠামোতে, মহাকাশযানকে 200 আলোকবর্ষ দূরত্ব \( 0.99c \) গতিতে অতিক্রম করতে যে সময় লাগবে, তা হলো:
\[ t = \frac{d}{v} = \frac{200 \text{ আলোকবর্ষ}}{0.99c} \approx 202 \text{ বছর} \]৩. নভোযানের কাঠামোতে অতিবাহিত সময় \( t' \) নির্ণয়:
\[ t' = \frac{t}{\gamma} = \frac{202 \text{ বছর}}{7.088} \approx 28.5 \text{ বছর} \]সুতরাং, নভোযানের ভেতরের মহাকাশচারীরা প্রায় 28.5 বছর অতিবাহিত হয়েছে বলে মনে করবে।
ফলাফল: নভোযানের কাঠামো থেকে পরিমাপ করা মহাকাশচারীদের বয়স হবে প্রায় 28 বছর। ✅
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