Calculating Min Δv for a Comet to Intersect Earth's Orbit

[bon]

Homework Statement

A comet in a circular orbit around the Sun has speed v0 and radius r0 = aRE ,
where RE is the radius of the Earth’s orbit and α is a constant > 1. The comet has its
velocity reduced by Δv in a collision that does not change its initial direction. Show
that the minimum value of Δv required to move the comet into an orbit which intersects
the Earth’s orbit is given by

delta v min = vo[1- root(2/(1+a))]

Homework Equations

The Attempt at a Solution

Not sure what the neatest way to proceed is?

Im guessing we look at energy and angular momentum..

after the collision, total energy is 1/2 m(vo - delta v)^2 - PE (which is unchanged)..

But when i put this into the Ellipse equation for energy i.e. E = 1/2m(dr/dt)^2 + J^2/... etc

and set dr/dt = 0 and J = mRe(vo-deltav)..i get everything cancelling out and leaving vo^2 = GM/Re..

not sure what I am meant to do basically!

 

[bon]

anyone?

 

[Mindscrape]

Classic Hohmann transfer orbit. You're trying to get what's known as the vis-visa orbit. Here's an example that will help, but not give you the answer. :)

http://en.wikipedia.org/wiki/Hohmann_transfer_orbit

 

[bon]

Classic Hohmann transfer orbit. You're trying to get what's known as the vis-visa orbit. Here's an example that will help, but not give you the answer. :)

http://en.wikipedia.org/wiki/Hohmann_transfer_orbit

Thanks..this was useful - but it lacked a derivation of the delta v expressions...

how can i work this out using conservation of energy and momentum?

Thanks

 

[Mindscrape]

Right, that's the question, how can you work that out using conservation laws? :p

I hate to be so hard up for information, but maybe you could post some more work so I could tell you where you went wrong.