A small meteor approaches the earth. When it is at a large distance it has velocity V∞ and impact parameter b. If Re is the radius of the earth and V0 is the escape velocity what is the condition...

A small meteor approaches the earth. When it is at a large distance it has velocity V∞ and impact parameter b. If Re is the radius of the earth and V0 is the escape velocity what is the condition that meteor strike the earth.

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Close approach to Earth perturbs a meteor’s trajectory in a big way. The Target Plane or b-plane approach for analysis of asteroid close approaches involves calculation of impact parameter b, which is the distance from the geocentre to the intercept of the asymptote on the plane of trajectory. It is in fact the minimum distance of the unperturbed trajectory of the meteor at its closest approach point.

The impact parameter alone does not reveal whether the perturbed trajectory of the meteor will intersect the figure of Earth or not.

This information can be extracted by scaling Earth’s radius according to:

`b(+)=r(+)sqrt(1+V_e^2/V_oo^2)`

where V_e is Earth’s escape velocity and V_oo, the unperturbed velocity of the meteor and r(+) is the Earth's radius.

With this we can say that a given trajectory impacts if b(+)>b and not otherwise.

Therefore, `bltr(+)sqrt(1+V_e^2/V_oo^2)`

This is the required condition that the meteor strikes the Earth.

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