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Telesnyi ugol

- chast' prostranstva, ogranichennaya konich. poverhnost'yu (poverhnost' obrazuyut pryamye, ishodyashie iz odnoi tochki i peresekayushie zamknutuyu napravlyayushuyu krivuyu, ris., a). T.u. izmeryaetsya otnosheniem ploshadi S toi chasti sfery s centrom v vershine O konich. poverhnosti, k-raya vyrezaetsya etim T.u., k kvadratu radiusa R sfery. Edinicy T.u. bezrazmerny, napr., T.u., zaklyuchayushii 1/8 prostranstva (oktant, ris., b), raven $4\pi R^2 /8R^2=\pi/2$ .

V astronomii primenyayutsya sleduyushie edinicy T.u.: steradian (sr), kvadratnyi gradus ( $\Box^\circ$ ), kvadratnaya minuta ( $\Box''$ ). Nebesnaya sfera soderzhit $4\pi$ sr, ili 129600 $/\pi^2 \Box^\circ=41252,96\Box^\circ$ ; 1 sr=32400 $/\pi^2 \Box^\circ=3282,81\Box^\circ$ .

Sferich. telo radiusom r, nahodyasheesya na rasstoyanii R ot tochki nablyudeniya, vyrezaet na nebesnoi sfere T.u., ravnyi $2\pi (1-\sqrt{1-r^2/R^2})$ sr; dlya $r\ll R$ T.u. raven $\pi (r/R)^2$ sr.

"Fizika Kosmosa", 1986
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