Question

2£®ÉèÏëijÔØÈË·É´¬ÈÆÒ»ÀàµØÐÐÐÇ×öÔÈËÙÔ²ÖÜÔ˶¯£¬Æä¹ìµÀ°ë¾¶¿ÉÊÓΪ¸ÃÐÐÐǰ뾶R£¬ÔØÈË·É´¬Ô˶¯ÖÜÆÚΪT£¬¸ÃÐÐÐDZíÃæµÄÖØÁ¦¼ÓËÙ¶ÈΪg£¬ÒýÁ¦³£Á¿ÎªG£¬Ôò£¨¡¡¡¡£©

• A£® ·É´¬µÄËÙ¶ÈÊÇÈÆÐÐÐÇ×öÔ²ÖÜÔ˶¯µÄ×î´óËÙ¶È
• B£® ¸ÃÐÐÐǵÄƽ¾ùÃܶȿɱíʾΪ$\frac{3¦Ð}{4GT^2}$
• C£® ¸ÃÐÐÐǵÄƽ¾ùÃܶȿɱíʾΪ$\frac{3g}{4¦ÐGR}$
• D£® ·É´¬×öÔ²ÖÜÔ˶¯µÄ°ë¾¶Ôö´ó£¬ÆäÔ˶¯ÖÜÆÚ½«¼õС

Answer 1

·ÖÎö ¸ù¾Ý·É´¬Êܵ½µÄÍòÓÐÒýÁ¦µÈÓÚ·É´¬ÐèÒªµÄÏòÐÄÁ¦£¬ÒÔ¼°¸ù¾ÝÐÇÇò±íÃæÖØÁ¦µÈÓÚÍòÓÐÒýÁ¦£¬¿ÉÁÐʽÇó½â£»

½â´ð ½â£ºA¡¢·É´¬ÈÆÐÐÐǸ½½ü×÷ÔÈËÙÔ²ÖÜÔ˶¯
    $G\frac{M{m}^{¡ä}¡ä}{{R}^{2}}={m}^{¡ä}¡ä\frac{{v}^{2}}{R}$
½âµÃ
  $v=\sqrt{\frac{GM}{R}}$£¬·É´¬µÄËÙ¶ÈËæ»·Èư뾶µÄÔö´ó¶ø¼õС£¬¿ÉÖª·É´¬µÄ¹ìµÀ°ë¾¶¿ÉÊÓΪ¸ÃÐÐÐǰ뾶Rʱ£¬·É´¬µÄËÙ¶ÈÊÇÈÆÐÐÐÇ×öÔ²ÖÜÔ˶¯µÄ×î´óËٶȣ®¹ÊAÕýÈ·£»
B¡¢ÐÐÐǶԷɴ¬µÄÍòÓÐÒýÁ¦Ìṩ·É´¬ËùÐèÏòÐÄÁ¦
       $G\frac{Mm}{r^2}=m{£¨\frac{2¦Ð}{T}£©^2}r$
½âµÃ
      $M=\frac{4{¦Ð}^{2}{r}^{3}}{G{T}^{2}}$
ÓÖ£ºM=¦ÑV=$¦Ñ•\frac{4}{3}¦Ð{R}^{3}$
ËùÒÔ¸ÃÐÐÐǵÄƽ¾ùÃܶȿɱíʾΪ$¦Ñ=\frac{M}{V}=\frac{\frac{4{¦Ð}^{2}{R}^{3}}{G{T}^{2}}}{\frac{4¦Ð{R}^{3}}{3}}=\frac{3¦Ð}{G{T}^{2}}$£®¹ÊB´íÎó£»
C¡¢ÖØÁ¦µÈÓÚÍòÓÐÒýÁ¦
      $m¡äg=\frac{GMm¡ä}{{R}^{2}}$
½âµÃ£ºM=$\frac{g{R}^{2}}{G}$
ËùÒÔ¸ÃÐÐÐǵÄƽ¾ùÃܶȿɱíʾΪ£º$¦Ñ=\frac{M}{V}=\frac{\frac{g{R}^{2}}{G}}{\frac{4¦Ð{R}^{3}}{3}}=\frac{3g}{4¦ÐGR}$£®¹ÊCÕýÈ·£»
D¡¢ÐÐÐǶԷɴ¬µÄÍòÓÐÒýÁ¦Ìṩ·É´¬ËùÐèÏòÐÄÁ¦
       $G\frac{Mm}{r^2}=m{£¨\frac{2¦Ð}{T}£©^2}r$
½âµÃ£ºT=$2¦Ð\sqrt{\frac{{r}^{3}}{GM}}$£¬¿ÉÖª·É´¬×öÔ²ÖÜÔ˶¯µÄ°ë¾¶Ôö´ó£¬ÆäÔ˶¯ÖÜÆÚ½«Ôö´ó£®¹ÊD´íÎó
¹ÊÑ¡£ºAC

µãÆÀ ¸ÃÌ⿼²éÍòÓÐÒýÁ¦¶¨ÂɵÄÒ»°ãÓ¦Ó㬽â´ð±¾Ìâ¹Ø¼üץסÐÇÇò±íÃæÖØÁ¦µÈÓÚÍòÓÐÒýÁ¦£¬·É´¬µÄÍòÓÐÒýÁ¦µÈÓÚÏòÐÄÁ¦£®