Improved wording of two-body problem page #38
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bryanwweber
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May 29, 2025
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Thanks for clarifying! I have a suggestion that sounds not natural to me, what do you think?
| where $\ddot{\vector{R}}$ is the **absolute acceleration** of the subscripted mass. Absolute means that the acceleration is taken relative to an inertial reference frame. This is important because Newton's second law only applies for absolute accelerations. | ||
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| Since the only force in this system is the gravitational attraction, the force is also equal to Newton's law of gravitation, {eq}`eq:newtons-law-of-gravitation`. The force of $m_2$ on $m_1$, $F_{12}$, points in the _positive_ direction of $\uvec{u}_r$. Because of Newton's third law, as represented by {eq}`eq:newtons-third-law-for-two-body`, the force of $m_1$ on $m_2$, $F_{21}$, points in the negative direction of $\uvec{u}_r$. This is shown in {eq}`eq:gravitational-force-two-body`: | ||
| Since the only force in this system is the gravitational attraction, the force may also be described by Newton's law of gravitation, {eq}`eq:newtons-law-of-gravitation`. The force of $m_2$ on $m_1$, $F_{12}$, points in the _positive_ direction of $\uvec{u}_r$. Because of Newton's third law, as represented by {eq}`eq:newtons-third-law-for-two-body`, the force of $m_1$ on $m_2$, $F_{21}$, points in the negative direction of $\uvec{u}_r$. This is shown in {eq}`eq:gravitational-force-two-body`: |
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I think I prefer "the force may be computed by Newton's..."
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Sounds good! Changed.
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Fixes #37 .