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 cc 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 cc 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 (cc) 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 cc 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 y;

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.