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Using Newton's law Fi,j=−Gmimjr→j−r→i|r→i−r→j|3F_{i,j} = -G m_i m_j \frac{\vec{r}_j - \vec{r}_i }{|\vec{r}_i - \vec{r}_j|^3} of gravitational attraction between two bodies ii and jj of masses mim_i and mjm_j at location r→i\vec{r}_i and r→j\vec{r}_j, write a function that computes the forces acting on each particle. $G = 6.67430\times10^{−11} N m^2/kg^2$ is the gravitational constant. The function shall take as input the current location of the particles as a 1D array xin of size $3*N$ for NN particles. The output is the 1D array of forces acting on each particles also as a $3*N$ length array.
Plain-text mathematical notation (without MathML)
Using Newton's law F_(i,j)=−Gm_(i)m_(j)((r)→_(j)−(r)→_(i))/(|(r)→_(i)−(r)→_(j)|³) of gravitational attraction between two bodies i and j of masses m_(i) and m_(j) at location (r)→_(i) and (r)→_(j), write a function that computes the forces acting on each particle. $G = 6.67430\times10^{−11} N m^2/kg^2$ is the gravitational constant. The function shall take as input the current location of the particles as a 1D array xin of size $3*N$ for N particles. The output is the 1D array of forces acting on each particles also as a $3*N$ length array.
Original LaTeX notation
Using Newton's law $F_{i,j} = -G m_i m_j \frac{\vec{r}_j - \vec{r}_i }{|\vec{r}_i - \vec{r}_j|^3}$ of gravitational attraction between two bodies $i$ and $j$ of masses $m_i$ and $m_j$ at location $\vec{r}_i$ and $\vec{r}_j$, write a function that computes the forces acting on each particle. $G = 6.67430\times10^{−11} N m^2/kg^2$ is the gravitational constant. The function shall take as input the current location of the particles as a 1D array xin of size $3*N$ for $N$ particles. The output is the 1D array of forces acting on each particles also as a $3*N$ length array.

step background

Background Gravity follows an inverse square law for the magnitude of the force bewtween two masses. The gravitional force between acting on the first mass m1m_1 of masses m1m_1 and m2m_2 separated by a vector r→\vec{r} of length rr is: F1→=−Gm1m2r2r→r \vec{F_1} = - \frac{G m_1 m_2}{r^2} \frac{\vec{r}}{r} where $G = 6.67430\times10^{−11} N m^2/kg^2$ is the gravitational constant, r→r\frac{\vec{r}}{r} is the unit vector pointing from mass m1m_1 to mass m2m_2.
Plain-text mathematical notation (without MathML)
Background
Gravity follows an inverse square law for the magnitude of the force bewtween two masses. The gravitional force between acting on the first mass m₁ of masses m₁ and m₂ separated by a vector (r)→ of length r is:

(F₁)→=−(Gm₁m₂)/(r²)((r)→)/(r)

where $G = 6.67430\times10^{−11} N m^2/kg^2$ is the gravitational constant, ((r)→)/(r) is the unit vector pointing from mass m₁ to mass m₂.
Original LaTeX notation
Background
Gravity follows an inverse square law for the magnitude of the force bewtween two masses. The gravitional force between acting on the first mass $m_1$ of masses $m_1$ and $m_2$ separated by a vector $\vec{r}$ of length $r$ is:

$$
\vec{F_1} = - \frac{G m_1 m_2}{r^2} \frac{\vec{r}}{r}
$$

where $G = 6.67430\times10^{−11} N m^2/kg^2$ is the gravitational constant, $\frac{\vec{r}}{r}$ is the unit vector pointing from mass $m_1$ to mass $m_2$.

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Source and history

upstream_id / Original problem ID
49.1
task_id
b454c81d-d0d0-58d9-a731-b0e0acf9d493
task_key
dev--38b5a2e7-b9f1-5c81-aa87-6c04903a3eb1--49~2e1
task_revision_id
5
config / split
/ dev

Official source

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