50 
The N.Z. Journal of Science and Technology. 
[Feb. 
Example 5 .—To find the maximum angle of projection in order that a 
particle with parabolic velocity projected from a point in the orbit of 
Neptune may just graze the surface of the Sun. 
SA _ 1 
SP “ 6452 ’ 
sin 2 a = 
sin a = 
1 
6452’ 
1 
8(433 ‘ 
a = nearly 43b 
This is about 80*33 times the angle which the radius of the Sun subtends 
at this distance. So gravity increases the chance of collision 6,452 times. 
(iii.) K < k. 
When the initial kinetol exceeds the parabolic the curve will be an 
hyperbola whatever the angle of projection. 
Since at every point on the path 
v 
2 
2 fJL 
T 
\ 
. t 
a 
= 2(Jfc-K). 
2a = 
/X 
k- K 
K 
k- K °’ 
which is constant whatever the angle of projection. 
