Question

State the universal law of gravitation and
derive its mathematical expression. (detail)​

Answer 1

ʜʟᴏ ᴍᴀᴛᴇ

ᴛʜᴇ ᴜɴɪᴠᴇʀsᴀʟ ʟᴀᴡ ᴏғ ɢʀᴀᴠɪᴛᴀᴛɪᴏɴ sᴛᴀᴛᴇs ᴛʜᴀᴛ ᴛʜᴇʀᴇ ɪs ᴀ ғᴏʀᴄᴇ ᴏғ ᴀᴛᴛʀᴀᴄᴛɪᴏɴ ʙᴇᴛᴡᴇᴇɴ ᴛᴡᴏ ᴍᴀssᴇs sᴇᴘᴀʀᴀᴛᴇᴅ ʙʏ sᴏᴍᴇ ᴅɪsᴛᴀɴᴄᴇ. ᴛʜᴇ ɢʀᴀᴠɪᴛᴀᴛɪᴏɴᴀʟ ғᴏʀᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴛᴡᴏ ʙᴏᴅɪᴇs ɪs ᴅɪʀᴇᴄᴛʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ ᴘʀᴏᴅᴜᴄᴛ ᴏғ ᴛʜᴇɪʀ ᴍᴀssᴇs ᴀɴᴅ ɪɴᴠᴇʀsᴇʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ sϙᴜᴀʀᴇ ᴏғ ᴛʜᴇ ᴅɪsᴛᴀɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴛʜᴇᴍ.

ᴍᴀᴛʜᴇᴍᴀᴛɪᴄᴀʟʟʏ,

ғ = ɢᴍ1ᴍ1/ʀ²

ᴡʜᴇʀᴇ, ɢ ɪs ᴛʜᴇ ᴜɴɪᴠᴇʀsᴀʟ ɢʀᴀᴠɪᴛᴀᴛɪᴏɴᴀʟ ᴄᴏɴsᴛᴀɴᴛ, ᴍ1 ᴀɴᴅ ᴍ1 ᴀʀᴇ ᴛʜᴇ ᴍᴀssᴇs sᴇᴘᴀʀᴀᴛᴇᴅ ʙʏ ᴀ ᴅɪsᴛᴀɴᴄᴇ ʀ.

ᴛʜᴇ ᴜɴɪᴠᴇʀsᴀʟ ʟᴀᴡ ᴏғ ɢʀᴀᴠɪᴛᴀᴛɪᴏɴ ɪs ᴀᴘᴘʟɪᴇᴅ ɪɴ ᴛʜᴇ sᴛᴜᴅʏ ᴏғ ᴍᴏᴛɪᴏɴ ᴏғ ᴏʙᴊᴇᴄᴛs ɪɴ ᴛʜᴇ ᴘʀᴇsᴇɴᴄᴇ ᴏғ ɢʀᴀᴠɪᴛᴀᴛɪᴏɴᴀʟ ғɪᴇʟᴅ. ᴍᴏᴛɪᴏɴ ᴏғ ᴀsᴛʀᴏɴᴏᴍɪᴄᴀʟ ʙᴏᴅɪᴇs ᴀʀᴇ ᴄᴀʟᴄᴜʟᴀᴛᴇᴅ ᴀɴᴅ ᴀʟsᴏ ᴘʀᴇᴅɪᴄᴛᴇᴅ ᴜsɪɴɢ ᴛʜɪs ʟᴀᴡ.

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