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Jan7-13, 08:19 PM
P: 1,398
Quote Quote by Simon Bridge View Post

You need 11.2kmps to escape the surface of the Earth - but still bound to the Sun.
To escape the Sun as well, you need 42.1kmps residual speed ... so, <waves hands around> 53.3kmps would get you out of the solar system from anywhere bound to the Earth.

If you get too precise, you have to take the planetary dynamics into account.
Anything else is an approximation.
There are two problems here.

1. The earth is already moving with about 30km/s around the sun. You only need to have about 12 km/s left after escaping the earth.

2. If you leave the surface of the earth with speed v (v > 11.2 km/s),
you will have kinetic energy (1/2)mv^2 with respect to the earth. The residual energy after getting far away from the earth will be (1/2) m (v^2 - 11.2^2), and this will need to be equal to the kinetic energy of the 12km/s residual speed you need,

so you get v^2 - 11.2^2 = 12^2 => v^2 = (11.2^2 + 12^2) => v = 16.4 km/s

This will be a speed of about 46.4 km/s with respect to the sun