Whakaoti i te 3(9.81)=6.67(10^-11)(m/r^2)-(w^2)r

$$3 ( 9.81 ) = 6.67 ( 10 ^ { - 11 } ) ( \frac { m } { r ^ { 2 } } ) - ( w ^ { 2 } ) r$$

Whakaoti mō m

$$m=\frac{100000000000r^{2}\left(100rw^{2}+2943\right)}{667}$$

$$r\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te r^{2}.

$$3\times 9.81r^{2}=6.67\times 10^{-11}m-w^{2}rr^{2}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 2 kia riro ai te 3.

$$3\times 9.81r^{2}=6.67\times 10^{-11}m-w^{2}r^{3}$$

Whakareatia te 3 ki te 9.81, ka 29.43.

$$29.43r^{2}=6.67\times 10^{-11}m-w^{2}r^{3}$$

Tātaihia te 10 mā te pū o -11, kia riro ko \frac{1}{100000000000}.

$$29.43r^{2}=6.67\times \frac{1}{100000000000}m-w^{2}r^{3}$$

Whakareatia te 6.67 ki te \frac{1}{100000000000}, ka \frac{667}{10000000000000}.

$$29.43r^{2}=\frac{667}{10000000000000}m-w^{2}r^{3}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$\frac{667}{10000000000000}m-w^{2}r^{3}=29.43r^{2}$$

Me tāpiri te w^{2}r^{3} ki ngā taha e rua.

$$\frac{667}{10000000000000}m=29.43r^{2}+w^{2}r^{3}$$

He hanga arowhānui tō te whārite.

$$\frac{667}{10000000000000}m=w^{2}r^{3}+\frac{2943r^{2}}{100}$$

Whakawehea ngā taha e rua o te whārite ki te \frac{667}{10000000000000}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{\frac{667}{10000000000000}m}{\frac{667}{10000000000000}}=\frac{r^{2}\left(rw^{2}+29.43\right)}{\frac{667}{10000000000000}}$$

Mā te whakawehe ki te \frac{667}{10000000000000} ka wetekia te whakareanga ki te \frac{667}{10000000000000}.

$$m=\frac{r^{2}\left(rw^{2}+29.43\right)}{\frac{667}{10000000000000}}$$

Whakawehe r^{2}\left(29.43+w^{2}r\right) ki te \frac{667}{10000000000000} mā te whakarea r^{2}\left(29.43+w^{2}r\right) ki te tau huripoki o \frac{667}{10000000000000}.

$$m=\frac{10000000000000r^{2}\left(rw^{2}+29.43\right)}{667}$$