# Ka honua a me ka pi0817

$$r_1 = 6370km$$ i ka honua (ma ke ʻano he sphere me $$r_1 = 6370km$$ ) a me kahi pea (ma ke ʻano he sphere me $$r_2 = 2mm$$ ) a $$r_2 = 2mm$$ i ke kaula ma luna o ka equator e moe pono ia ma luna. I kēia manawa hoʻolōʻihi ʻoe i nā kaula ʻelua i hoʻokahi mika i kēlā me kēia. E moe pono loa nā kaula ʻelua i luna o ka equator - ʻaʻole lākou e moe moe hou ma ka ʻili, akā e kau i luna o ka equator. Pehea ke kiʻekiʻena o ka papa e lana ai ke kaula ma luna o ka honua, pehea ke kiʻekiʻena o ka pi?

Loaʻa i nā kaula ʻelua ka lōʻihi mua:

$$l_1 = 2\cdot 6370 km \cdot \pi \Leftrightarrow r_1 = 6370 km = \frac{l_1}{2 \cdot \pi}$$

e like me

$$l_2 = 2 \cdot 2mm \cdot \pi \Leftrightarrow r_2 = 2mm = \frac{l_2}{2 \cdot \pi}.$$

Akā i kēia manawa aia ma hope o ka hoʻolōʻihi

$$r_{1 NEU} = \frac{l_1 + 1m}{2\cdot \pi}$$

e like me

$$r_{2 NEU} = \frac{l_2 + 1m}{2\cdot \pi}.$$

Akā kupaianaha kēia manawa

$$r_{1 NEU} - r_1 = \frac{l_1 + 1m}{2\cdot \pi} - \frac{l_1}{2\cdot \pi} = \frac{l_1 + 1m - l_1}{2 \cdot \pi} = \frac{1m}{2 \cdot \pi} = 0.159m$$

e like me

$$r_{2 NEU} - r_2 = \frac{l_2 + 1m}{2\cdot \pi} - \frac{l_2}{2\cdot \pi} = \frac{l_2 + 1m - l_2}{2 \cdot \pi} = \frac{1m}{2 \cdot \pi} = 0.159m.$$

Pēlā ka mamao mai ka ʻilikai i kūʻokoʻa i ka $$l_1$$ a i ʻole $$l_2$$ , ʻo ia hoʻi he kūʻokoʻa i ka radii $$r_1$$ a i ʻole $$r_2$$ nā ʻāpana. Penei ka pane kupaianaha: lana nā kaula ʻelua i ke kiʻekiʻe like $$0.159m$$ ) ma luna o ka ʻili.

Hope