Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

Solutions 181

We shall write the momentum conservation law

in projections on the x- and y-axes (Fig. 179):

10mv 1 = 11.mv2s,^ (1

mu = 1lmv2y.^ (2)

After the collision, the station goes over to an

elliptical orbit. The energy of the station with the

;

m

Fig. 179

meteorite stuck in it remains constant during the

motion in the elliptical orbit. Consequently,

11mM 11m

—G (v 2 +v 2 )

11mM

R ' 2 2 t

11M

= G V2

R/2 1- 2 ' '

where V is the velocity of the station at the momen t
of the closest proximity to the planet. Here we
have used the formula for the potential energy of
gravitational interaction of two bodies (of mass
m 1 and m 2 ): W —Gmimdr. According to
Kepler's second law, the velocity V is connected to

(3)