Question

Imagine sitting with two friends around a table, where all three of you have different masses. Calculate the magnitude and direction of the gravitational field in the centre of the table due to your three masses

Answer 1

Answer on Question #82946, Physics / Electromagnetism

Question:

Imagine sitting with two friends around a table, where all three of you have different masses.

Calculate the magnitude and direction of the gravitational field in the centre of the table due to your three masses

Solution:

The intensity of the gravitational field equals to $\overline{I} = G\frac{m}{r^3}\overline{r}$ where $m$ is a mass producing the field, $\overline{r}$ is the proper radius-vector, directed from the center to $m$ . Respectively the net intensity is $\overline{I}_n = G\sum_{1}^{3}\frac{m_i}{r_i^3}\overline{r_i}$ , the magnitude of the gravitational field in the centre $M$ is $M = \mathrm{mod}(\overline{I}_n)$ and the direction corresponds to $\overline{I}_n$ direction.

The answer:

The net intensity is $\overline{I}_n = G\sum_{1}^{3}\frac{m_i}{r_i^3}\overline{r_i}$ , the magnitude of the gravitational field in the centre M is $M = \mathrm{mod}(\overline{I}_n)$ and the direction corresponds to $\overline{I}_n$ direction.

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