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| <h3 id="back-link"><a href="../../#1.4">$\leftarrow$Back</a></h3> | | <h3 id="back-link"><a href="../../#1.4">$\leftarrow$Back</a></h3> |
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| <h3> Statement </h3> | | <h3> Statement </h3> |
| <p> | | <p> |
| $1.4.3.$ One of the dust cloud particles (particle $A$) is at rest, and all the others are flying away from it in different directions with velocities proportional to the distances from them to particle $A$. What motion pattern will an observer detect when moving with particle $B$? | | $1.4.3.$ One of the dust cloud particles (particle $A$) is at rest, and all the others are flying away from it in different directions with velocities proportional to the distances from them to particle $A$. What motion pattern will an observer detect when moving with particle $B$? |
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| <h3>Solution</h3> | | <h3>Solution</h3> |
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| <p > | | <p > |
| He will find that all particles are moving away from him with a speed directly proportional to the distance from particle $B$ to them. | | He will find that all particles are moving away from him with a speed directly proportional to the distance from particle $B$ to them. |
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| <p > | | <p > |
| This can be proven as follows: write down the speeds of particle $B$ and an arbitrary particle $C$ in the reference frame of particle $A$, and then go to the reference frame of particle $B$, and make sure that the speed of particle $C$ in this reference frame is proportional to the distance between particles $B$ and $C$. Moreover, it is proportional with the same coefficient as in the reference frame of particle $A$. | | This can be proven as follows: write down the speeds of particle $B$ and an arbitrary particle $C$ in the reference frame of particle $A$, and then go to the reference frame of particle $B$, and make sure that the speed of particle $C$ in this reference frame is proportional to the distance between particles $B$ and $C$. Moreover, it is proportional with the same coefficient as in the reference frame of particle $A$. |
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| <h4>Answer</h4> | | <h4>Answer</h4> |
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| Exactly the same as an observer moving with particle $A$. | | Exactly the same as an observer moving with particle $A$. |
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