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Universal Gravitation

Problem 1.233

Find approximately the third cosmic velocity v3v_{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.

Reveal Answer
1.233. v3≈2v12+(V2‾−1)2V12≈17 km/s.v_{3} \approx \sqrt{2 v_{1}^{2}+(V \overline{2}-1)^{2} V_{1}^{2}} \approx 17 \quad \mathrm{~km} / \mathrm{s} . Here v12=v_{1}^{2}= =γME/R,ME=\gamma M_{E} / R, M_{E} and RR are the mass and the radius of the Earth; V12=γMB/r,MˉSV_{1}^{2}=\gamma M_{B} / r, \bar{M}_{S} is the mass of the Sun, rr is the radius of the Earth's orbit.
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