12-11-2017, 12:59 PM

Introduction

The program CONICAP determines three characteristics of a conic section:

Eccentricity:

E = 0, circle

0 < E < 1, ellipse

E = 1, parabola (this case is not covered)

E > 1, hyperbola

Periapsis (Perigee):

The point on the conic section where it is closest to a primary focus (which is designated at one of the two foci F or F’).

Apoapsis (Apogee):

The point on the conic section where it is furthest away from a primary focus. Note for a hyperbola and a parabola, the apogee is ∞.

The inputs are the lengths of the semi-major axis (A) and the semi-minor axis (P). For a hyperbola, input A as negative.

HP Prime Program CONICAP

Examples

A = 8, P = 3 (Ellipse)

Perigee 1.67544467966

Apogee 14.3245553203

Eccentricity 0.790569415042

A = -8, P = 3 (Hyperbola)

Perigee 1.38083151968

Apogee N/A

Eccentricity 1.17260393996

Source:

Roger R. Bate, Donald D. Mueller, Jerry E. White. Fundamentals of Astrodynamics Dover Publications: New York. 1971. ISBN-13: 978-0-486-60061-1

The program CONICAP determines three characteristics of a conic section:

Eccentricity:

E = 0, circle

0 < E < 1, ellipse

E = 1, parabola (this case is not covered)

E > 1, hyperbola

Periapsis (Perigee):

The point on the conic section where it is closest to a primary focus (which is designated at one of the two foci F or F’).

Apoapsis (Apogee):

The point on the conic section where it is furthest away from a primary focus. Note for a hyperbola and a parabola, the apogee is ∞.

The inputs are the lengths of the semi-major axis (A) and the semi-minor axis (P). For a hyperbola, input A as negative.

HP Prime Program CONICAP

Code:

EXPORT CONICAP(A,P)

BEGIN

// EWS 2017-12-10

// Fundamentals Of Astrodynamics

// ABS(A)≥P

LOCAL E;

E:=√(1-P/A);

PRINT();

PRINT("Perigee: "+STRING(A*(1-E)));

IF A≥0 THEN

PRINT("Apogee: "+STRING(A*(1+E)));

END;

PRINT("Eccentricity: "+E);

IF E==0 THEN

PRINT("Circle");

END;

IF E>0 AND E<1 THEN

PRINT("Ellipse");

END;

IF E>1 THEN

PRINT("Hyperbola");

END;

END;

Examples

A = 8, P = 3 (Ellipse)

Perigee 1.67544467966

Apogee 14.3245553203

Eccentricity 0.790569415042

A = -8, P = 3 (Hyperbola)

Perigee 1.38083151968

Apogee N/A

Eccentricity 1.17260393996

Source:

Roger R. Bate, Donald D. Mueller, Jerry E. White. Fundamentals of Astrodynamics Dover Publications: New York. 1971. ISBN-13: 978-0-486-60061-1