System and method for assessing the risk of conjunction of a rocket body with orbiting and non-orbiting platforms

1. A target access volume determination apparatus comprising:

a rocket processing unit, wherein the rocket processing unit comprises a first processor and wherein the first processor is configured with software executable instructions to cause the rocket processing unit to perform operations comprising:

receiving a latitude and an altitude of a launcher from which the rocket will be launched and a rocket velocity and a specified trajectory;

receiving a target altitude (alt sat ) and a topocentric firing azimuth (AZ topocentric ) from a set of desired target altitudes and topocentric firing azimuths;

initializing the processor with values for a launcher firing angle relative to a horizon (φ), wherein φ is small and positive, an increment of φ (dφ), a range of the rocket (α) equal to zero, and an altitude at burnout (alt bo ) equal to the altitude of the rocket launcher (alt launcher );

for each desired target altitude (alt sat ) and topocentric firing azimuth (AZ topocentric ), determining:

a magnitude of a rotating earth rocket velocity (V sez );

whether the rocket has sufficient energy to reach alt sat and insufficient energy to achieve orbit;

when the rocket has sufficient energy to reach alt sat and insufficient energy to achieve orbit:

determining a value of the rocket's angular range α and an eccentricity (ecc);

determining the rocket's a, ecc, α, β, and TOF in an inertial frame, wherein a is the semi-major axis, β is a target's off-nadir angle to the rocket launcher, and TOF is a time of flight of the rocket from the rocket launcher to the target;

determining when the current value of α is greater than a previous value of α;

when the current α is less than or equal to the previous value of α, then setting α MAX equal to the previous value of α and a MAX , ecc MAX , β MAX , and TOF MAX equal to the previous values of a, ecc, β, and TOF; and

when the current α is greater than the previous value of α, then incrementing φ by dφ and determine a next value of α; and

an access volume processing unit, wherein the access volume processing unit comprises a second processor and wherein the second processor is configured with software executable instructions to cause the access volume processing unit to perform operations comprising:

for each desired target altitude (alt sat ) and topocentric firing azimuth (AZ topocentric ):

receiving α MAX a MAX , ecc MAX , β MAX , and TOF MAX ;

determining a latitude of the satellite lat sat and a longitudinal offset (ΔN) corresponding to α MAX a MAX , ecc MAX , β MAX , and TOF MAX ;

identifying a point defined by alt sat , lat sat , and ΔN in an inertial frame relative to a launcher location; and

defining a volume surface from the points determined for each alt sat and AZ topocentric in the set of desired target altitudes and topocentric firing azimuths; and

a display and alert processing unit, wherein display and alert processing unit comprises a third processor and wherein the third processor is configured with software executable instructions to cause the display and alert processing unit to perform operations comprising:

receiving the volume surface from the access volume processing unit;

generating a visual representation of a access volume; and

sending the visual representation to a display device for display.

2. The apparatus of claim 1 , wherein the software executable instructions further initialize the first processor with an intercept mode selected from the group of an intercept on descent, an intercept on ascent, and a quick-ascent intercept.

3. The apparatus of claim 1 , wherein the third processor is further configured with software executable instructions to cause the display and alert processing unit to perform operations comprising:

determining whether the targeted platform is in the access volume; and

issuing an alert when the targeted platform is in the access volume.

4. The apparatus of claim 3 , wherein the instruction for issuing an alert comprises an instruction for issuing an alert using at least one media selected from the group consisting of a visual alert, a text alert and an audio alert.

5. The apparatus of claim 1 , wherein the target is selected from the group consisting of an orbiting platform and a ballistic projectile.

6. A method for determining the accessibility of a target to an earth-launched rocket for a specified trajectory comprising:

receiving at a rocket processing unit a latitude and an altitude of a launcher from which the rocket will be launched and a velocity of the rocket, wherein the rocket processing unit comprises a first processor;

receiving at the rocket processing unit a target altitude (alt sat ) and a topocentric firing azimuth (AZ topocentric ) from a set of desired target altitudes and topocentric firing azimuths;

initializing the first processor with values for a launcher firing angle relative to a horizon (φ), wherein φ is small and positive, an increment of φ (dφ), a range of the rocket (α) equal to zero, and an altitude at burnout (alt bo ) equal to the altitude of the rocket launcher (alt launcher );

for each desired target altitude (alt sat ) and topocentric firing azimuth (AZ topocentric ):

using the first processor to determine a magnitude of a rotating earth rocket velocity (V sez ); and

using the first processor to determine whether the rocket has sufficient energy to reach alt sat and insufficient energy to achieve orbit;

when the rocket has sufficient energy to reach alt sat and insufficient energy to achieve orbit:

using the first processor to determine a value of the rocket's angular range α and an eccentricity (ecc);

using the first processor to determine the rocket's a, ecc, α, β, and TOF in an inertial frame, wherein a is the semi-major axis, β is a target's off-nadir angle to the rocket launcher, and TOF is a time of flight of the rocket from the rocket launcher to the target; and

using the first processor to determine when the current value of α is greater than a previous value of α;

when the current α is less than or equal to the previous value of α, then using the first processor for setting α MAX equal to the previous value of α and a MAX , ecc MAX , β MAX , and TOF MAX equal to the previous values of a, ecc, β, and TOF; and

when the current α is greater than the previous value of α, then using the first processor for incrementing φ by dφ and for determining a next value of α; and

for each desired target altitude (alt sat ) and topocentric firing azimuth (AZ topocentric ):

receiving at an access volume processing unit α MAX a MAX , ecc MAX , β MAX , and TOF MAX ,

wherein the access volume processing unit comprises a second processor;

using the second processor to determine a latitude of the satellite lat sat and a longitudinal offset (ΔN) corresponding to α MAX a MAX , ecc MAX , β MAX , and TOF MAX ;

using the second processor to identify a point defined by alt sat , lat sat , and ΔN in an inertial frame relative to a launcher location; and

using the second processor to define a volume surface from the points determined for each alt sat and AZ topocentric ; and

receiving the volume surface from the access volume processing unit at a display and alert processing unit, wherein the display and alert processing unit comprises a third processor;

using the third processor to generate a visual representation of a access volume; and

using the third processor to send the visual representation to a display device for display.

7. The method of claim 1 further comprising initializing the first processor with an intercept mode selected from the group of an intercept on descent, an intercept on ascent, and a quick ascent intercept.

8. The method of claim 1 further comprising:

using the third processor to determine whether the targeted platform is in the access volume; and

using the third processor to issue an alert when the targeted platform is in the access volume.

9. The method of claim 8 , wherein issuing an alert comprises issuing an alert using at least one media selected from the group consisting of a visual alert, a text alert and an audio alert.

10. The method of claim 1 , wherein the target is selected from the group consisting of an orbiting platform and a ballistic projectile.

11. A target access volume determination apparatus comprising:

a rocket processing unit, wherein the rocket processing unit comprises a first processor and wherein the first processor is configured with software executable instructions to cause the rocket processing unit to perform operations comprising:

receiving a set of desired arrival azimuths of a rocket γ, a muzzle velocity V m of the rocket, an altitude of the rocket launcher (alt launcher ) from which the rocket will be launched, a specific launch trajectory, and a target altitude alt sat ;

initializing the first processor by setting a value for a rotating earth rocket velocity (V sez ) to V m ;

for each desired arrival azimuth of a rocket γ at the target altitude alt sat :

(a) determining the rocket's a, ecc, α, β, and TOF in an inertial frame, wherein a is the semi-major axis, β is a target's off-nadir angle to the rocket launcher, and TOF is a time of flight of the rocket from the rocket launcher to the target; and

(b) determining a current value of the rocket's angular range α;

(c) when the current α is not equal to π or to 0, then determining a current value of the rotating earth rocket velocity (V sez ); and

(d) determining when the current value of V sez is approximately equal to a just previous value of V sez ;

when the current value of V sez is not approximately equal to a just previous value of V sez , then initializing the first processor with the current V sez and performing operations (a)-(d); and

when the current value of V sez is approximately equal to the just previous value of V sez , then determining lat launcher and longitudinal offset (ΔN); and

an access volume processing unit, wherein the access volume processing unit comprises a second processor and wherein the second processor is configured with software executable instructions to cause the access volume processing unit to perform operations comprising:

receiving the lat launcher and longitudinal offset (ΔN), wherein lat launcher and longitudinal offset (ΔN) determine a point in an inertial frame relative to the target; and

identifying a accessibility region constructed from points determined for the selected alt sat over the set of desired arrival azimuths γ; and

a display and alert processing unit, wherein display and alert processing unit comprises a third processor and wherein the third processor is configured with software executable instructions to cause the display and alert processing unit to perform operations comprising:

receiving the region from the access accessibility processing unit;

using the third processor to generate a visual representation of a accessibility region; and

using the third processor to send the visual representation to a display device for display.

12. The apparatus of claim 11 further comprising initializing the first processor with an intercept mode selected from the group of an intercept on descent, an intercept on ascent, and a quick ascent intercept.

13. The apparatus of claim 11 further comprising:

using the third processor to determine whether a rocket launcher is in the accessibility region; and

using the third processor to issue an alert when the rocket launcher is in the access volume.

14. The apparatus of claim 13 , wherein issuing an alert comprises issuing an alert using at least one media selected from the group consisting of a visual alert, a text alert and an audio alert.

15. The apparatus of claim 11 , wherein the target is selected from the group consisting of an orbiting platform and a ballistic projectile.

16. A method for determining the accessibility of a target to an earth-launched rocket comprising:

receiving at a rocket processing unit a set of desired arrival azimuths of a rocket γ, a muzzle velocity V m of the rocket, an altitude of the rocket launcher (alt launcher ) from which the rocket will be launched, and a target altitude alt sat , wherein the rocket processing unit comprises a first processor;

initializing the first processor by setting a value for a rotating earth rocket velocity (V sez ) to V m ;

for each desired arrival azimuth of a rocket γ at the target altitude alt sat :

(a) using the first processor to determine the rocket's a, ecc, α, β, and TOF in an inertial frame, wherein a is the semi-major axis, β is a target's off-nadir angle to the rocket launcher, and TOF is a time of flight of the rocket from the rocket launcher to the target; and

(b) using the first processor to determine a current value of the rocket's angular range α;

(c) when the current α is not equal to π or to 0, then using the first processor to determine a current value of the rotating earth rocket velocity (V sez ); and

(d) using the first processor to determine when the current value of V sez is approximately equal to a just previous value of V sez ;

when the current value of V sez is not approximately equal to a just previous value of V sez , then initializing the first processor with the current V sez and performing steps (a)-(d);

when the current value of V sez is approximately equal to the just previous value of V sez , then using the first processor to determine lat launcher and longitudinal offset (ΔN);

receiving at a accessibility processing unit the lat launcher and longitudinal offset (ΔN), wherein the access volume processing unit comprises a second processor and wherein lat launcher and longitudinal offset (ΔN) determine a point in an inertial frame relative to the target;

using the second processor to identify a accessibility region constructed from points determined for the selected alt sat over the set of desired arrival azimuths γ;

receiving the region from the access accessibility processing unit at a display and alert processing unit, wherein the display and alert processing unit comprises a third processor;

using the third processor to generate a visual representation of a accessibility region; and

using the third processor to send the visual representation to a display device for display.

17. The method of claim 11 further comprising initializing the first processor with an intercept mode selected from the group of an intercept on descent, an intercept on ascent, and a quick-ascent intercept.

18. The method of claim 11 further comprising:

using the third processor to determine whether a rocket launcher is in the accessibility region; and

using the third processor to issue an alert when the rocket launcher is in the access volume.

19. The method of claim 13 , wherein issuing an alert comprises issuing an alert using at least one media selected from the group consisting of a visual alert, a text alert and an audio alert.

20. The method of claim 11 , wherein the target is selected from the group consisting of an orbiting platform and a ballistic projectile.