Edits to “Statement”, “Answer”
en/2.2.7.md
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| @@ -1,11 +1,5 @@ | |||
| ### Statement | |||
| − | $2.2.7.$ [Insert the problem statement] | ||
| − | |||
| − | ### Solution | ||
| − | |||
| − | ### Statement | ||
| − | |||
| $2.2.7.$ During observations from Earth, it is possible to determine only the radial velocity of partner stars that are part of a binary star (i.e., the projection of the velocity onto the Earth-star line). Upon measurements, the values of the radial velocity $v_1$ and $u_1$ of the partner stars of the binary star were obtained. During repeated measurements taken a year later, the values of this velocity turned out to be $v_2$ and $u_2$. Find the ratio of the masses of the partner stars comprising this binary star. Why is it necessary to change the calculations if the repeated measurement is taken after a month or half a year? | |||
| ### Solution | |||
| From the law of conservation of momentum $\vec{p}_1 = \vec{p}_2$: | |||
| $$m_1 v_1 + m_2 u_1 = m_1 v_2 + m_2 u_2$$ | |||
| $$m_1/m_2 = (u_2 - u_1)/(v_1 - v_2)$$ | |||
| If measuring not after a year, it is necessary to introduce a correction for the change in the position and velocity of the Earth, since the radial velocities are relative to the velocity of the Earth. | |||
| @@ -19,7 +13,3 @@Solution | |||
| #### Answer | |||
| $$\frac{m_1}{m_2} = \frac{u_2 - u_1}{v_1 - v_2}$$ | |||
| It is necessary to take into account the change in the Earth's velocity. | |||
| − | |||
| − | #### Answer | ||
| − | |||
| − | [Insert a concise answer or boxed result] | ||
| @@ -1,11 +1,5 @@ | |||
| ### Statement | ### Statement | ||
| $2.2.7.$ [Insert the problem statement] | |||
| ### Solution | |||
| ### Statement | |||
| $2.2.7.$ During observations from Earth, it is possible to determine only the radial velocity of partner stars that are part of a binary star (i.e., the projection of the velocity onto the Earth-star line). Upon measurements, the values of the radial velocity $v_1$ and $u_1$ of the partner stars of the binary star were obtained. During repeated measurements taken a year later, the values of this velocity turned out to be $v_2$ and $u_2$. Find the ratio of the masses of the partner stars comprising this binary star. Why is it necessary to change the calculations if the repeated measurement is taken after a month or half a year? | $2.2.7.$ During observations from Earth, it is possible to determine only the radial velocity of partner stars that are part of a binary star (i.e., the projection of the velocity onto the Earth-star line). Upon measurements, the values of the radial velocity $v_1$ and $u_1$ of the partner stars of the binary star were obtained. During repeated measurements taken a year later, the values of this velocity turned out to be $v_2$ and $u_2$. Find the ratio of the masses of the partner stars comprising this binary star. Why is it necessary to change the calculations if the repeated measurement is taken after a month or half a year? | ||
| ### Solution | ### Solution | ||
| From the law of conservation of momentum $\vec{p}_1 = \vec{p}_2$: | From the law of conservation of momentum $\vec{p}_1 = \vec{p}_2$: | ||
| $$m_1 v_1 + m_2 u_1 = m_1 v_2 + m_2 u_2$$ | $$m_1 v_1 + m_2 u_1 = m_1 v_2 + m_2 u_2$$ | ||
| $$m_1/m_2 = (u_2 - u_1)/(v_1 - v_2)$$ | $$m_1/m_2 = (u_2 - u_1)/(v_1 - v_2)$$ | ||
| If measuring not after a year, it is necessary to introduce a correction for the change in the position and velocity of the Earth, since the radial velocities are relative to the velocity of the Earth. | If measuring not after a year, it is necessary to introduce a correction for the change in the position and velocity of the Earth, since the radial velocities are relative to the velocity of the Earth. | ||
| @@ -19,7 +13,3 @@Solution | |||
| #### Answer | #### Answer | ||
| $$\frac{m_1}{m_2} = \frac{u_2 - u_1}{v_1 - v_2}$$ | $$\frac{m_1}{m_2} = \frac{u_2 - u_1}{v_1 - v_2}$$ | ||
| It is necessary to take into account the change in the Earth's velocity. | It is necessary to take into account the change in the Earth's velocity. | ||
| #### Answer | |||
| [Insert a concise answer or boxed result] | |||