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Dazed&Confused

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## Homework Statement

Suppose the asteroid of [other problem] has a mass of [itex]6 \times 10^{20} \textrm{kg} [/itex]. Find the proportional change in the kinetic energy of the Earth in this encounter. What is the change in the semi-major axis of the Earth's orbit? By how much is its orbital period lengthened?

Other problem:

Suppose the asteroid of [other problems] approaches the Earth with an impact parameter of [itex]5 R_E[/itex], where [itex]R_E[/itex] = Earth's radius, moving in the same plane and overtaking it. Find the distance of closest approach and the angle which the asteroid is scattered, in the frame of reference in which the Earth is at rest.

## Homework Equations

## The Attempt at a Solution

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The value of Earth's velocity is 28.9km/s and that of the comet is 38.6km/s. The angle of deflection was 18.4 degrees. I tried calculating

[tex] \dot{\textrm{R}} - \frac{m_1}{M} \dot{\textrm{r}} [/tex] to work out the new velocity and from that the energy change. The book's answer was [itex]3\times10^{-6}[/itex] whereas mine was [itex]59\times 10^{-6} [/itex]. I'm not sure if my approach is correct.