Whakaoti i te F=Gmm/r^2

$$F = \frac { G m m } { r ^ { 2 } }$$

Whakaoti mō G (complex solution)

$$\left\{\begin{matrix}G=\left(\frac{r}{m}\right)^{2}F\text{, }&m\neq 0\text{ and }r\neq 0\\G\in \mathrm{C}\text{, }&F=0\text{ and }m=0\text{ and }r\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$Fr^{2}=Gmm$$

Whakareatia te m ki te m, ka m^{2}.

$$Fr^{2}=Gm^{2}$$

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

$$Gm^{2}=Fr^{2}$$

He hanga arowhānui tō te whārite.

$$m^{2}G=Fr^{2}$$

Whakawehea ngā taha e rua ki te m^{2}.

$$\frac{m^{2}G}{m^{2}}=\frac{Fr^{2}}{m^{2}}$$

Mā te whakawehe ki te m^{2} ka wetekia te whakareanga ki te m^{2}.

$$G=\frac{Fr^{2}}{m^{2}}$$

Whakaoti mō G

$$\left\{\begin{matrix}G=\left(\frac{r}{m}\right)^{2}F\text{, }&m\neq 0\text{ and }r\neq 0\\G\in \mathrm{R}\text{, }&F=0\text{ and }m=0\text{ and }r\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$Fr^{2}=Gmm$$

Whakareatia te m ki te m, ka m^{2}.

$$Fr^{2}=Gm^{2}$$

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

$$Gm^{2}=Fr^{2}$$

He hanga arowhānui tō te whārite.

$$m^{2}G=Fr^{2}$$

Whakawehea ngā taha e rua ki te m^{2}.

$$\frac{m^{2}G}{m^{2}}=\frac{Fr^{2}}{m^{2}}$$

Mā te whakawehe ki te m^{2} ka wetekia te whakareanga ki te m^{2}.

$$G=\frac{Fr^{2}}{m^{2}}$$

Whakaoti mō F

$$F=\left(\frac{m}{r}\right)^{2}G$$

$$r\neq 0$$