Ex. 5. A particle of mass m is observed to move in a spiral oribit given by the equation r = Co, where
C is a constant. Is it moving in a central force field ? If it is so, find the force law.
Solution : The differential equation of the orbit (eq.(26) ] is given by
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ᴀ ᴘᴀʀᴛɪᴄʟᴇ ᴏғ ᴍᴀss ᴍ ɪs ᴏʙsᴇʀᴠᴇᴅ ᴛᴏ ᴍᴏᴠᴇ ɪɴ ᴀ sᴘɪʀᴀʟ ᴏʀɪʙɪᴛ ɢɪᴠᴇɴ ʙʏ ᴛʜᴇ ᴇǫᴜᴀᴛɪᴏɴ ʀ = ᴄᴏ, ᴡʜᴇʀᴇ
ᴄ ɪs ᴀ ᴄᴏɴsᴛᴀɴᴛ. ɪs ɪᴛ ᴍᴏᴠɪɴɢ ɪɴ
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The differential equation of the orbit (eq.(26) ] is given by
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