# If the radius of the Earth's orbit around the Sun is 150 million km, what is the speed of the Earth?

Mar 20, 2018

The gravitation force grant the centripetal force.

#### Explanation:

${F}_{g} = {F}_{c}$
${F}_{g} = \frac{G {M}_{s u n} {M}_{e a r t h}}{{R}^{2}}$ Newton gravitation law
where $G = 6.67 \cdot {10}^{- 11} {m}^{3} / \left(k g \cdot s\right)$, $R = 1.5 \cdot {10}^{11} m , {M}_{s u n} = 2 \cdot {10}^{30}$
$\frac{G {M}_{s u n} {M}_{e a r t h}}{{R}^{2}} = {M}_{e a r t h} {v}^{2} / R$
${v}^{2} = G {M}_{s u n} / R$
$v = 29.8 \frac{k m}{s}$
${v}_{m e a n} = 29 , 783 \frac{k m}{s}$ sorce: https://en.wikipedia.org/wiki/Earth