A mission for disaster monitoring is launched in a circular Sun-Synchronous with semi-major axis a = : 7027.46558 km. a. Compute the orbit period. Also determind how many revolutions the spacecraft completes in a repeat cycle of 19 days? [15 points] b. Compute the distance in km between two consecutive tracks at the equator and show that the minimum distance between tracks in one repeat cycle is 143.125 km. [15 points] c. The Earth orbit angular velocity around the Sun is 0.9860/day. Compute the inclination required for this orbit to be Sun-synchronous, considering that the secular variation of the right ascension of ascending node due to Earth's oblateness is given by 3nJ₂R² 2a² (1 — e²)² in which n is the mean motion of the orbit. Show that the orbit is retrograde. [20 points] d. For this spacecraft, compute the minimum field of view of an onboard camera that enables the global coverage of the Earth. In your calculations you can assume a flat Earth and the camera always pointing in the nadir direction. Propose a change to the repeat cycle pattern to enable global coverage in case the minimum field of view available is 10° [20 points] dΩ dt Relevant Data 1 day = 86400 s Earth gravitational parameter E - 3.986×105 km³s-2 (cos i), Earth mean radius RE 6378.14 km Earth oblateness J₂ = 1.0823×10-³ Earth rotational angular velocity we 7.2921×10-5 rad/s =
A mission for disaster monitoring is launched in a circular Sun-Synchronous with semi-major axis a = : 7027.46558 km. a. Compute the orbit period. Also determind how many revolutions the spacecraft completes in a repeat cycle of 19 days? [15 points] b. Compute the distance in km between two consecutive tracks at the equator and show that the minimum distance between tracks in one repeat cycle is 143.125 km. [15 points] c. The Earth orbit angular velocity around the Sun is 0.9860/day. Compute the inclination required for this orbit to be Sun-synchronous, considering that the secular variation of the right ascension of ascending node due to Earth's oblateness is given by 3nJ₂R² 2a² (1 — e²)² in which n is the mean motion of the orbit. Show that the orbit is retrograde. [20 points] d. For this spacecraft, compute the minimum field of view of an onboard camera that enables the global coverage of the Earth. In your calculations you can assume a flat Earth and the camera always pointing in the nadir direction. Propose a change to the repeat cycle pattern to enable global coverage in case the minimum field of view available is 10° [20 points] dΩ dt Relevant Data 1 day = 86400 s Earth gravitational parameter E - 3.986×105 km³s-2 (cos i), Earth mean radius RE 6378.14 km Earth oblateness J₂ = 1.0823×10-³ Earth rotational angular velocity we 7.2921×10-5 rad/s =
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
![A mission for disaster monitoring is launched in a circular Sun-Synchronous with semi-major axis
a = : 7027.46558 km.
a. Compute the orbit period. Also determind how many revolutions the spacecraft completes in a
repeat cycle of 19 days? [15 points]
b. Compute the distance in km between two consecutive tracks at the equator and show that the
minimum distance between tracks in one repeat cycle is 143.125 km. [15 points]
c. The Earth orbit angular velocity around the Sun is 0.9860/day. Compute the inclination
required for this orbit to be Sun-synchronous, considering that the secular variation of the right
ascension of ascending node due to Earth's oblateness is given by
3nJ₂R²
2a² (1 — e²)²
in which n is the mean motion of the orbit. Show that the orbit is retrograde. [20 points]
d. For this spacecraft, compute the minimum field of view of an onboard camera that enables the
global coverage of the Earth. In your calculations you can assume a flat Earth and the camera
always pointing in the nadir direction. Propose a change to the repeat cycle pattern to enable
global coverage in case the minimum field of view available is 10° [20 points]
dΩ
dt
Relevant Data
1 day = 86400 s
Earth gravitational parameter E
-
3.986×105 km³s-2
(cos i),
Earth mean radius RE 6378.14 km
Earth oblateness J₂ = 1.0823×10-³
Earth rotational angular velocity we 7.2921×10-5 rad/s
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1798f175-bb80-4b77-a3c8-d787f888ab8d%2Facdf4714-8bbc-4f69-87fe-6a2f87d52101%2Fzq2i37_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A mission for disaster monitoring is launched in a circular Sun-Synchronous with semi-major axis
a = : 7027.46558 km.
a. Compute the orbit period. Also determind how many revolutions the spacecraft completes in a
repeat cycle of 19 days? [15 points]
b. Compute the distance in km between two consecutive tracks at the equator and show that the
minimum distance between tracks in one repeat cycle is 143.125 km. [15 points]
c. The Earth orbit angular velocity around the Sun is 0.9860/day. Compute the inclination
required for this orbit to be Sun-synchronous, considering that the secular variation of the right
ascension of ascending node due to Earth's oblateness is given by
3nJ₂R²
2a² (1 — e²)²
in which n is the mean motion of the orbit. Show that the orbit is retrograde. [20 points]
d. For this spacecraft, compute the minimum field of view of an onboard camera that enables the
global coverage of the Earth. In your calculations you can assume a flat Earth and the camera
always pointing in the nadir direction. Propose a change to the repeat cycle pattern to enable
global coverage in case the minimum field of view available is 10° [20 points]
dΩ
dt
Relevant Data
1 day = 86400 s
Earth gravitational parameter E
-
3.986×105 km³s-2
(cos i),
Earth mean radius RE 6378.14 km
Earth oblateness J₂ = 1.0823×10-³
Earth rotational angular velocity we 7.2921×10-5 rad/s
=
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