Is answer in BMW book for problem 4.3 wrong?

Proof that book problem answer is wrong:

Since r0 and v0 are perpendicular, then satellite must be at aporigee or perigee.

But ro = I + J, hence |ro| = sqrt(2)

and vo = 2K hence |vo| = 2

v^2 u

Energy = ------ - ----

2 r

Hence Energy (calculated at perigee) = 4/2 – 1/sqrt(2) = 1.2928932

Since E>0, this is a hyperbola. Then must be a perigee.

u

Energy = - ----- ---(1)

2a

To find ‘a’, Plug Energy in (1), and noting that u=1, we get

1

1.2928932 = - -----

2a

hence a = -0.3867295 DU

| I J K |

h = r0 x v0 = | 1 1 0 | = I (2) – J (2)

| 0 0 2 |

hence h = sqrt(4+4) = sqrt(8)

h^2

Now, p = ---- = h^2

u

Hence p = 8

p

To find e, from rp = ---------------

1 + e cos(0)

(I can also use p=a(1-e^2) to find e).

since rp = r0 = sqrt(2), then 1+e=8/sqrt(2)

e = 8/sqrt(2) – 1 = 4.656854

Now we can find r when satellite traveled 60 degree.

p 8

r = --------------- = ---------------------- = 2.4035377 DU

1 + e cos(60) 1 + 4.656854 cos(60)

Now I find v when satellite traveled 60 degrees

From

v^2 1

--- - --- = Energy

2 r

But we found Energy and r from above, and since Energy is constant, so solve for new v

v^2 = 2 (1.2928932 + 1/2.4035377)

v^2 = 3.417893173

v = 1.84875449 DU/TU

Now, the book gives this answer as to the velocity:

v = -0.348 I – 0.348 J + 1.5 K

then v = 1.57867286 DU/TU

as you can see, this answer does not agree with my calculation.

I do not see where I am going wrong. Is the book wrong or right?