All Problems Universal Gravitation
Problem 1.233
Find approximately the third cosmic velocity \(v_{3}\), i.e. the minimum velocity that has to be imparted to a body relative to the Earth's surface to drive it out of the Solar system. The rotation of the Earth about its own axis is to be neglected.
1.233. \(v_{3} \approx \sqrt{2 v_{1}^{2}+(V \overline{2}-1)^{2} V_{1}^{2}} \approx 17 \quad \mathrm{~km} / \mathrm{s} .\) Here \(v_{1}^{2}=\) \(=\gamma M_{E} / R, M_{E}\) and \(R\) are the mass and the radius of the Earth; \(V_{1}^{2}=\gamma M_{B} / r, \bar{M}_{S}\) is the mass of the Sun, \(r\) is the radius of the Earth's orbit.