Consider a gun or rifle fired directly upwards. My original question was what speed would be required to escape the Earth.
The escape velocity from the surface of the Earth is the classic $$v_e = \sqrt{ 2GM \over r } \approx 11,000 \text{ m/s}$$ and bullets typically (see for example) leave the muzzle with a maximum speed one order of magnitude lower, ~$1,000$ m/s. Terminal velocity of bullets in STP is another magnitude lower, ~$100$ m/s.
Even if a bullet were fired with speed $v_e$ that of course would not be sufficient due to drag which would slow the bullet down. So a theoretical required speed $v_T > v_e$.
- If the bullet were fired with anything close to $v_e$ or $v_T$, would it would burn up very rapidly in STP? I understand that rockets typically don't achieve anything like $v_e$ until they are high in the atmosphere at least in part for this reason
- And hence is there no speed possible in realistic conditions with which a bullet could be fire and escape the Earth?
- If it is possible, what model of drag should one use to calculate $v_T$ and concretely, does anyone have an estimate of its value?
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