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en/2.6.12.md
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| + | ### Statement | ||
| + | |||
| + | $2.6.12.$ [Insert the problem statement] | ||
| + | |||
| + | ### Solution | ||
| + | |||
| + | For a circular orbit, the gravitational force provides the centripetal force:\ | ||
| + | $\frac{GmM}{r^2}=mw^2 r$\ | ||
| + | where $G$ is the gravitational constant, $M$ is the mass of the Sun, $m$ the asteroid's mass, $r$ is the orbital radius and $w$ is the angular velocity\ | ||
| + | we get\ | ||
| + | $\frac{GM}{r^2}=w^2 r$\ | ||
| + | and from that\ | ||
| + | $r=(\frac{GM}{w^2})^1/3$ | ||
| + | |||
| + | #### Answer | ||
| + | |||
| + | [Insert a concise answer or boxed result] | ||
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| ### Statement | |||
| $2.6.12.$ [Insert the problem statement] | |||
| ### Solution | |||
| For a circular orbit, the gravitational force provides the centripetal force:\ | |||
| $\frac{GmM}{r^2}=mw^2 r$\ | |||
| where $G$ is the gravitational constant, $M$ is the mass of the Sun, $m$ the asteroid's mass, $r$ is the orbital radius and $w$ is the angular velocity\ | |||
| we get\ | |||
| $\frac{GM}{r^2}=w^2 r$\ | |||
| and from that\ | |||
| $r=(\frac{GM}{w^2})^1/3$ | |||
| #### Answer | |||
| [Insert a concise answer or boxed result] | |||