 | Physik M 513.805 (511.015) |
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| Physik M 513.805 (511.015) |
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Gravitational potential energyThe gravitational force $\vec{F}_{12}$ exerted by object 1 on object 2 is, \[ \begin{equation} \large \vec{F}_{12}=-\frac{Gm_1m_2}{|\vec{r}_1-\vec{r}_2|^2}\hat{r}_{12}, \end{equation} \]Where $G = 6.6726 \times 10^{-11}$ N m²/kg² is the gravitational constant, $\hat{r}_{12}$ is the unit vector that points from object 1 to object 2, $m_1$ and $m_2$ are the masses of the two objects, and $|\vec{r}_1-\vec{r}_2|=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$ is the distance between the two objects. A satellite of mass kg is moved from a circular orbit 000 km from the center of the earth to another circular orbit 000 km from the center of the earth. By how much has the gravitational potential energy of the satellite been increased? The mass of the earth is $5.976\times 10^{24}$ kg, and the radius of the earth is $6.378\times 10^{6}$ m. |