Whakaoti i te 1/2*910^2=667*10^-11*598*10^24/r

$$\frac { 1 } { 2 } \times 910 ^ { 2 } = 667 \times 10 ^ { - 11 } \times \frac { 598 \times 10 ^ { 24 } } { r }$$

Whakaoti mō r

$$r=\frac{6136400000000000}{637}\approx 9.633281005 \cdot 10^{12}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe r ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2r, arā, te tauraro pātahi he tino iti rawa te kitea o 2,r.

$$\frac{1}{2}\times 910^{2}\times 2r=667\times 10^{-11}\times 2\times 598\times 10^{24}$$

Tātaihia te 910 mā te pū o 2, kia riro ko 828100.

$$\frac{1}{2}\times 828100\times 2r=667\times 10^{-11}\times 2\times 598\times 10^{24}$$

Whakareatia te \frac{1}{2} ki te 828100, ka 414050.

$$414050\times 2r=667\times 10^{-11}\times 2\times 598\times 10^{24}$$

Whakareatia te 414050 ki te 2, ka 828100.

$$828100r=667\times 10^{-11}\times 2\times 598\times 10^{24}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te -11 me te 24 kia riro ai te 13.

$$828100r=667\times 10^{13}\times 2\times 598$$

Tātaihia te 10 mā te pū o 13, kia riro ko 10000000000000.

$$828100r=667\times 10000000000000\times 2\times 598$$

Whakareatia te 667 ki te 10000000000000, ka 6670000000000000.

$$828100r=6670000000000000\times 2\times 598$$

Whakareatia te 6670000000000000 ki te 2, ka 13340000000000000.

$$828100r=13340000000000000\times 598$$

Whakareatia te 13340000000000000 ki te 598, ka 7977320000000000000.

$$828100r=7977320000000000000$$

Whakawehea ngā taha e rua ki te 828100.

$$r=\frac{7977320000000000000}{828100}$$

Whakahekea te hautanga \frac{7977320000000000000}{828100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 1300.

$$r=\frac{6136400000000000}{637}$$