Tải bản đầy đủ - 0 (trang)
B.3 Online Ephemeris Project on PHAs, NEOs, and Other Celestial Objects

B.3 Online Ephemeris Project on PHAs, NEOs, and Other Celestial Objects

Tải bản đầy đủ - 0trang

Appendix B Projects



355



Part 1: Questions About PHAs, NEOs, and the Torino Scale

1. What is a potentially hazardous asteroid (PHA)? How many PHAs are known?

2. Which near-earth objects (NEOs) came within a nominal miss distance of 0.5

LD (lunar distance) of the earth since 12/12/12? What was the nominal closest

approach (CA) distance of each of these objects? What was the date of each of

these closest approaches? Include a copy of the one page in the table from the

website with the appropriate information “highlighted.”

3. Which NEO discovered in 2012 came within the closest nominal miss distance

of the earth since 11/10/12? What was the nominal CA distance of this object

and what was the date of its CA? Highlight the appropriate information in the

page from the website supplied in your answer to question 2.

4. Which of the known PHAs will come closest to the earth, considering the

nominal miss distance, in the next 25 years? What date will this object make its

CA to the earth and how close will this object approach the earth? Include a

copy of the one page in the table from the website with the appropriate

information (asteroid name, date of CA, and nominal miss distance)

“highlighted.”

5a. What is the Torino scale?

5b. Which asteroids have a value on the Torino scale greater than zero?

6. Explore the ssd and neo websites to find something else that is interesting.

What is one interesting item that you found?

Part 2: Computation of Rise, Transit, and Set Times for Earth-Based

Observatories

1. At what time UT did Mars rise as seen from an observatory in Los Angeles, CA,

on 12/11/2013?

2. Was Mars optically observable from a site in Los Angeles, CA, as it set on

12/11/2013? Explain why or why not.

3. What constellation was Mars in when it set on 12/11/2013?

4. What are the latitude and longitude of Los Angeles, CA?

Part 3: Questions About Trojan Asteroids

1. Which Trojan asteroids have a semimajor axis that satisfies the conditions

5.328 AU



a < 5.3305 AU?



2. What are the semimajor axis, eccentricity, inclination, and argument of perihelion of each of these asteroids?

For these two questions, include a copy of the one page in the table from the

website with the appropriate information (object full name, e, a, i, and peri)

“highlighted.”

3. Which of the asteroids found in the answer to question 1 of Part 3 has an IAU

name? What is the IAU name for each one?



356



Appendix B Projects



Part 4: Use of Orbit Diagrams in the Neo Website

Follow the procedure for visualizing the orbit of a comet or asteroid via an orbit

diagram in the neo website to answer the following questions with respect to the

comet Lulin (2007N3), nicknamed the “green comet.”

1. On what date did comet Lulin pass through perihelion and what was its distance

from the sun at that point?

2. When (approximate date) did comet Lulin make its closest approach to Mars?

3. What is the eccentricity of comet Lulin’s orbit? Make a copy of the table that

gives this value, “highlight” the appropriate entry in the table, and submit the

table with your answer. Note how close comet Lulin’s orbit is to being parabolic.

4. Is comet Lulin’s orbit posigrade or retrograde? Note how close comet Lulin’s

orbit is to being in the ecliptic plane.

References for Appendix B: Cunningham, MathWorks website, MATLAB

Tutorial website, neo website, ssd website.



Appendix C Additional Penzo Parametric Plots



C.1



Objectives



The P2 parameters discussed so far are either constraints or have been directly

connected with a parametric representation of these constraints. They were chosen

to minimize the parametric representation required and to enhance intuitive knowledge of free-return circumlunar trajectories.

The reference “An Analysis of Free-Flight Circumlunar Trajectories” by Paul A.

Penzo gives parametric plots of additional parameters, including the following:

1. Injection velocity versus the outward time of flight for various positions of the

moon in its orbit (Fig. C.1).

2. Parking orbit altitude versus injection velocity for fixed injection energies C3

(Fig. C.2).

3. Probe-moon-earth angle versus the outward time of flight for various positions

of the moon in its orbit (Fig. C.3).

4. Hyperbolic excess velocity versus the outward time of flight for fixed outwardphase inclinations and various positions of the moon in its orbit (Fig. C.4).

5. Earth-moon-probe-angle at the spacecraft’s exit from the SoI versus the return

time of flight for various positions of the moon in its orbit (Figs. C.5 and C.6).

6. Components of the impact vector B for constant outward times of flight

(Fig. C.7).

These parameters provide velocity information at the earth and at the moon and

information about entrance and exit angles at the moon’s sphere of influence.



C.2



Injection Velocities and the PME Angle



Figure C.1 presents the injection velocities required for specified outward times of

flight. The injection altitude is fixed at 600,000 ft (183 km). This velocity is

essentially a function of only the time of flight and distance of the moon. Figure C.2

can be used to convert these injection velocities to other altitudes while holding the

energy fixed.

# Springer International Publishing Switzerland 2015

G.R. Hintz, Orbital Mechanics and Astrodynamics,

DOI 10.1007/978-3-319-09444-1



357



358



Appendix C Additional Penzo Parametric Plots

PARKING ORBIT RADIAL DISTANCE = 0.215 × 108 FEET



36,100



ANALYTIC PROGRAM

EXACT PROGRAM



INJECTION VELOCITY V0 (FPS)



36,050



36,000



35,950



C



35,900

D

B

A′

A



35,850

60



70

80

90

OUTWARD TIME OF FLIGHT T0 (HOURS)



Fig. C.1 Injection velocity versus outward time of flight for various positions of the moon

in its orbit



Considering parameters in the moon phase, Fig. C.3 presents the probe-moonearth (PME) angle of the asymptotic velocity vector with the moon-to-earth line at

the time of pericynthion passage for various positions of the moon in its orbit. We

consider two specific types of launch trajectories:

Case I for all trajectories in which the spacecraft is launched ccw wrt the earth and

so that the outward-phase conic lies in the moon’s orbit plane.

Case II for which the spacecraft is launched normal to the moon’s orbit plane. The

symmetry relationship makes it immaterial as to whether the spacecraft

approaches the moon from above or below the moon’s orbit plane.



Appendix C Additional Penzo Parametric Plots



C3 = −.30



−.25



−.20



−.15



−.10



−.05



359



−0



Fig. C.2 Parking orbit altitude versus the injection velocity for fixed injection energies C3



Case I and Case II represent outward-phase launches in the moon’s orbit plane

and normal to the moon’s plane, respectively. Qualitatively, we can deduce that the

longer the flight time is to the moon the larger the PME angle. Also, from Fig. C.1,

since shorter distances of the moon require lower injection velocities for a given

flight time, the PME angle will increase for these shorter distances.



C.3



Moon-Phase Parameters: v1, EMP Angle at SoI Exit,

and the B-Plane



Figure C.4 presents the moon-phase hyperbolic excess velocity as a function of the

outward time of flight and the distance of the moon. The injection velocity is

essentially independent of the outward inclination, but the v1 is not. For Case II,

this velocity is from 400 to 800 fps greater than that for Case I. Exact integration

(precision) software was run to provide a comparison with the analytic software.

The exact integration software consistently produced a higher value for v1 than the

analytic program.

An estimate for the earth-moon-probe (EMP) angle at exit from the SoI is given

in Figs. C.5 and C.6. The behavior of this angle is similar to the PME angle. Three



30

50



40



50



60



70



80



C



D



B



A′



A



60

70

80

90

OUTWARD TIME OF FLIGHT T0 (HOURS)



ANALYTIC PROGRAM

EXACT PROGRAM



50



C



D



B



A′



A



60

70

80

90

OUTWARD TIME OF FLIGHT T0 (HOURS)



CASE II



Fig. C.3 Probe-moon-earth angle versus the outward time of flight for various positions of the moon in its orbit



PME ANGLE (DEGREES)



CASE I



360

Appendix C Additional Penzo Parametric Plots



Tài liệu bạn tìm kiếm đã sẵn sàng tải về

B.3 Online Ephemeris Project on PHAs, NEOs, and Other Celestial Objects

Tải bản đầy đủ ngay(0 tr)

×