What velocity relitive to the earth is required to escape th

Solution

There is an escape velocity for every object with mass. Now, we wouldn\'t think about it in terms of escaping the system, but an object. So, for our solar system, we\'d be escaping the Sun.

Now, the escape velocity depends on where you start. This is because gravity affects objects less when they are distanced from the center of the mass. So, if you were to start at the surface of the Sun (696,342 km equatorial radius), your escape velocity would be ~617.5 km/sec. If you started at Earth\'s orbit (1.496 x 10⁸ km), your escape velocity would only be a snail\'s pace of 42.1 km/sec.

As we need to find out escape velocity from earth’s orbit, the escape velocity from the Sun from earth’s orbit can be calculated as

v_S = (2/r)

where is standard gravitational parameter and for sun it is equal to 1.327124 x 10¹¹ km³s^-2

Substituting values into the equation results in:

v_S = (2*1.327124 x 10¹¹/1.496*10⁸) km/s

v_S = (17.738*10²) km/s

v_S = 42.1 km/s

This is the escape velocity from the Sun from earth’s orbit.

Now Earth is moving at 29.78 km/s so to escape the solar system on a parabolic path from earth\'s orbit, we need 42.1 km/s velocity in the direction of Earth\'s motion, so 42.1-29.78 = 12.32 km/s

Escape velocity relative to the earth to escape the solar system on a parabolic path from earth\'s orbit = 12.32 km/s.