When exploring a small planet with a radius of 770 km and a mass of 8.48 x 10^30 kg a small spacecraft with a mass of 8170 kg is placed in an elliptical orbit around it. When the spacecraft is at a distance of 2530 km from the center of mass of the small planet, it has an orbital speed of 453 m/s. What is the orbital speed, in meters per second, when the spacecraft is at a distance of 12090 km from the small planet?
The orbital speed of a spacecraft at different points in its elliptical orbit around a small planet can be found using the conservation of angular momentum (mvr), which remains constant throughout the orbit.
\[L_1 = L_2\]
\[L_1 = mv_1r_1\]
\[L_2 = mv_2r_2\]
\[\Rightarrow v_1 r_1 = v_2 r_2\]
\[\Rightarrow v_2 = \frac{453 \cdot 2530 \cdot 10^3}{12090 \cdot 10^3} = 94.797 \, \text{m/s}\]
