VELOCITY.— H, 189 



Fall from Infinite Space=2, 022,008 feet per second. 

 " " 2o,ooo,ooor =2,022,008 " " '' 

 " " i,ooo,ooor =2,022,007 " " " 



But 20,000, ooor is nearly half the distance, to the nearest sun, while 1,000,- 

 ooor is only 157 times the distance of Neptune. It follows that if a comet makes 

 near approach to the solar surface on parabola or hyperbola, it cannot be deter- 

 mined whether it began to fall from distance equal to i or 2,000, for a body 

 traversing a right line from 10, ooor to the Sun will collide with velocity of 

 2,021,957 leet, and from 2o,ooo,ooor — 2,022,008 feet per second, the difference 

 being 51 feet, ratios of distances fallen being as i to 2,000. The comet of 1843 

 passed perihelion at a distance of — "One-fifth the Sun's semi-diameter," New- 

 comb and Holden's "Astronomy," p. 406. Calculating, using formula, — V=G 

 Xby square root of quotient of distance divided by square of distance, we found 

 velocity of comet at perihelion to have been 349.6 miles per second. But, it 

 traversed a parabola and vanished from the solar system ; doing so because its 

 velocity was too great to permit it to yield to solar attraction and fall on the Sun; 

 and because it was not moving on the line A B at epoch. Velocity and direc- 

 tion decided whether it disappear on parabola or fall on ellipse and make future 

 circuits. 



Its velocity — too rapid by forty-one per cent, evolved centrifugal tendency 

 surpassing gravity, and bore it away on a parabolic curve. Making orbital ve- 

 locity (V) when centrifugal tendency and gravity balance, we find V=:GXt>y 

 square root of quotient of distance from Sun's centre divided by twice the square 

 of distance=247.2 miles per second. (Distauce=i.2). Had the comet this 

 velocity at instant of perihelion, it would have fallen into an ellipse whose major- 

 axis would have direction determined by angle made with radius vector by the 

 comet's path, With such velocity, and direction at a right angle, — then would 

 comet have made future revolutions on a circle. The result 247. 2 may be obtained 

 with less computation, for 349. 6—1. 4i42=:247. 2; but this i. 4142 is the square 

 root of 2; hence orbital velocity at a distance from the Sun's centre where centri- 

 fugal tendency equals gravity, is to fall from an infinite radius to that distance as 

 I is to the square root of 2. Or, — velocity on a closed, as circle or ellipse, is to 

 velocity on an open conic as parabola or hyperbola as i : 1.4142, an excess of 

 .4142 velocity over circular or elliptical orbital velocity, being required to thrust 

 abody beyond the solar system to a distance equal to that whence it begun to 

 fall. 



Place a cannon at right angles to a radius of the earth, fire a ball with a ve- 

 locity of 4.90833 miles per second, and in absence of air, it will not fall, but 

 revolve like a satellite. Elevate the ball to a distance equal to the earth's mean 

 radius — 3958 miles— and let fall; it will strike with velocity of 4.90833 miles per 

 second. 



The earth's distance from the Sun is 92,882,000 miles, and velocity 18.4927 

 miles per second. 



