escape velocity of solar system

azwraith69

1. The problem statement, all variables and given/known data
A projectile is fired from the earth in the direction of the earth’s motion around
the sun. what minimum speed must the projectile have relative to the earth to escape the
SOLAR SYSTEM? Ignore the earth’s rotation.


2. Relevant equations

escape velocity = sqt[(2G x mass of sun) / earth's distance from sun, 1 AU]

3. The attempt at a solution
is the solution that simple? or did I miss some concepts? I think only the sun's gravitation is considered...

thanks

kuruman

The expression you have is the escape velocity for an object placed where the Earth is and at rest with respect to the Sun, i.e. has zero kinetic energy relative to the Sun. This is not the case for a projectile fired from the Earth because the Earth is moving relative to the Sun.

azwraith69

Thanks.. what should i do then? should i add earth's velocity in its orbit? how exactly will i compute for that? thanks...

i will submit this after 6 hours,, so i really need direct answers.. cant reply anymore.. thanks in advance

kuruman

You don't have to reply if you can't, but we don't give direct answers either. Yes, you need to add the Earth's speed because the projectile is fired in the same direction as the Earth is moving. To find the Earth's speed, consider this: how far does the Earth travel in its orbit in one year?

azwraith69

ok sorry,,

but,, do i really need to add earth's speed? I need the escape velocity relative to earth..

thanks

kuruman

As I said, the equation that you quoted gives the speed that the projectile must have if it were at rest relative to the Sun. If it were already moving relative to the Sun (as in this case), would it need a higher or lower speed than the equation gives?