Design and performance of the flash satellite “Ladybeetle-1”

Abstract

The first satellite which can flash Morse code on orbit is introduced in this paper. The design of the system includes light energy estimation, attitude mode design, elevation angle analysis and flash time design. It is a 100 kg satellite with two LED arrays on 547 km. When it flashes, the satellite points to the observation location. The LED rays flash as the rule of Morse code. The satellite was sent to the orbit in Dec 2018 and the test of flash was completed within one month after then. The photo taken by star sensor can compare the apparent magnitude by the gray level. The results of the analysis show that the satellite can achieve 0 apparent magnitude, which is consistent with the design of the system. As a meaningful scientific experiment, “Ladybeetle-1” links space technology with popular science education and also provides a reference for space applications.

Keywords

Flash satellite Morse code attitude mode design light energy estimation ground observation

Introduction

The satellite, “LadyBeetle-1”, was launched into space on the 7th December, 2018. The It is used for science popularization of science education by shortening the distance between space technology and the public. It weights 100 kg, containing 6 cameras, 2 LED arrays, and communication payload. In this paper, a scheme of on-orbit flash Morse code is proposed. Equipped with a high-power spotlight array, the satellite can achieve 0 apparent magnitude. By using the principle of Morse code, different meanings are expressed by long and short flashes. The project is designed and configured based on commercial devices. The attitude determination and control system(ADCS) is implemented, also with whole platform including batteries and data storage and transmission system.

One special function of “LadyBeetle-1” is “flash mode”. This paper introduces the design and verification of this mode. The creative idea of the function is originated from the aerospace science fiction enthusiasts. In order to achieve the brightness visible to the naked eyes on the ground, the LED array is designed based on the principles of optics. The ADCS also designs a work-mode named “Earth pointing”. When we want to send messages through the flash of the satellite, the previously prepared tele-control instruction is sent to the satellite. The control instruction includes the location of our ground observation and the time we want to see the flash.

The observation on the ground can verify the correctness and effectiveness of the system design. The flash is not only visible to the naked eyes, but also can be caught by the ordinary household SLR camera to take photos. The star sensor made by TY-space company is also used to take photos. The apparent magnitude of the satellite is calculated to proved that the designed system is effective enough to achieve 0 apparent magnitude.

After on-orbit test, the function of satellile is open to the public. Astrophotographers took a lot of excellent photose of the flash. Observation activities for astrophotographers and astronomers have also attracted educators, and students, as well as many children, who observed the flash of “LadyBeetle-1”. In the announcement of the observation activities, the time, location, azimuth and elevation are predicted, except for the code, which is always kept as secret before the flash. The audience are curious about the code. The satellite has inspired people's interests in the sky. Due to the reflection of sunlight, some other spacecrafts can be seen in the night, such as Iridium and International Space Station. But “LadyBeetle-1” can give people a short sentence by Morse code. The satellite also provides customized services, as people can upload their blessings to it for flash, which may be the most innovative and interesting function of the satellite. When running across the galaxy, “Ladybeelte-1” makes science closer to the public,esp. the sudents and children.

Design of the mission

Light energy estimation

The height of “LadyBeetle-1” is 547 km, and its orbital period is about 95 minutes. The original expectation of the apparent magnitude was set to 0 and close to Vega. The area with a radius <20 km is chosen to watch the flash. According to the duration of satellite passing by the place, the flash time is set to 2 min. The most important mission is to estimate the luminance we need.

The solar illuminance constant ( $E_{s c}$ ), is equal to $1.28 \times 10^{5}$ lx¹ when there is no cloud in the sky and the sun is directly above the head. The apparent magnitude of the sun² can be calculated as

m_{Sun} = - 2.5 \log_{10} (\frac{1.28 \times 10^{5}}{2.56 \times 10^{- 6}}) = - 26.74

(1)

where

2.56 \times 10^{- 6}

lx is the reference flux in the same band such as Vega having apparent magnitude almost zero. In Ref.,3 the star of apparent magnitude 0 provides

2.08 \times 10^{- 6}

lx at the earth's surface.

One of the most important factors is the influence of the atmosphere on the transmittance. The data from simulation shows the transmittance is affected by the latitude and the wavelength. Since “Ladybeetle-1” serves the users in China, we only consider the mid-latitude region and the differences between city and countryside. The urban visibility is 5 km, with the seasons of summer and winter when there is no rain and cloud. The transmittance curve is Figure 1.

Figure 1.

Transmittance curve (Left: summer, urban; Right: winter, urban).

The countryside visibility is 23 km, with the seasons of summer and winter when there is no rain and cloud, the transmittance curve is as Figure 2.

Figure 2.

Transmittance curve (Left: summer, countryside; Right: winter, countryside).

Different wavelength of light has different transmittance, and result to the different wavelength sensitivity of the human eyes. From Figures 1 and 2, we know that the transmittance in the contryside in winter is the best. In this situation, the spectrum analysis is shown as Table 1.

Table 1.

Spectrum analysis.

Wavelength (nm)	430–480	480–530	530–580	580–630	630–680	680–730
Percentage	17.24%	17.24%	24.14%	24.14%	13.8%	3.44%
Vision rate	0.06	0.46	0.95	0.57	0.11	0.001
Transmittance	0.5670	0.6235	0.6540	0.6852	0.7320	0.7342

In Table 1, the transmittances of different wavelength are given. Consider the sensitivity of the human eyes to the light, the transmittance can be chosen as 0.6, which is closed to it in the wavelength range of 480–530.

According to the constraint about the weight and power of the satellite, we design two LED arrays and install them on the satellite. The arrays are assembled on the satellite as indicated in the photo below in Figure 3.

Figure 3.

LED arrays on “Ladybeetle-1”.

The luminous flux of the LED arrays can achieve 44000 lm. After the light source simulation, the max light intensity is $3.016 \times 10^{6}$ cd. Based on the consideration of machining and installation errors, the angle is set to 3.6°, which corresponds 34 km on the ground. Then the solid angle can be calculated

Ω = \frac{π \times {(547 \times \tan (3.6 °))}^{2}}{547^{2}} = 0.0124

(2)

When the transmittance is 0.6, the ground illumination can be calculated as below

E_{0} = \frac{3.016 \times 10^{6} \times 0.0124}{π \times {(547 \times 10^{3} \times \tan (3.6))}^{2}} \times 0.6 \approx 6 .0 \times 10^{- 6} lx

(3)

The above analysis after equation (1) shows that the illumination of 0 apparent magnitude star is $2 .56 \times 10^{-6}$ lx on the ground. Since $E_{0} > 2.56 \times 10^{- 6}$ lx, the LED arrays have enough light intensity to complete the flash mission.

“Earth pointing” mode design

The ADCS has several modes for different missions and most of them depend on the missions.⁴ When the LED array is flashing in the space, the normal of the plane should point to the place to reduce the loss of light intensity. This mode is like the LED gazing into the place where we want to watch the flash.

Before the satellite flies into the shadow of the earth, it must collect enough electric power in the attitude mode called “Sun pointing”.⁵ The normal mode in the umbra time is “Earth stable” mode, which is designed for the antenna sending data to the ground station. In this mode, the body frame coincides with the orbit frame. Since the orbit of “Ladybeetle-1” is 547 km SSO, it flies from south to the earth in the umbra time. The satellite should maneuver to the “Earth pointing” mode in advance. If the “power on” of the LED time is set to T0, the process of the mission is shown as Table 2.

Table 2.

Process of mode changing in the mission.

Time	Mode	Remarks	Light power
<T0-300 s	Earth stable	Auto	Power off
T0-300 s	Maneuver	Manual	Power Off
T0-300 + Tm1(Tm1 < 300 s)	Earth pointing	Auto	Power Off
T0	Earth pointing	Manual	Power On
T0 + 120 s	Earth pointing	Auto	Power Off
T0 + 150 s	Maneuver	Manual	Power Off
T0+Tm2	Earth stable	Auto	Power Off

We use $p$ to denote the frame of “Earth pointing” mode. The place $D$ is calculated by the command from the station, contains the latitude, longitude and height of the location. The point $O_{I}$ is the center of the inertial frame. The point $O_{O}$ is the mass center of the satellite. The vector $r_{O D}$ points from $O_{O}$ to $D$ . The vector $r_{I D}$ points from $O_{I}$ to $D$ . The vector $r_{I O}$ points from $O_{I}$ to $O_{O}$ . The schematic diagram is shown in Figure 4.

Figure 4.

Schematic diagram of the “Earth pointing” mode.

The relation of those three vectors above can be written as

r_{O D}^{I} = r_{I D}^{I} - r_{I O}^{I}

(4)

where

I

means the inertial frame. The axis

z_{p}

can be written as

z_{p}^{I} = \frac{r_{O D}^{I}}{| r_{O D}^{I} |}

(5)

If there is no mission in the umbra time, the default mode of ADCS is “Earth stable” which mean the body frame $O_{b} X_{b} Y_{b} Z_{b}$ is in coincidence with the orbit frame. When the system receives the command maneuver to the “Earth pointing” mode, the ADCS immediately changes into the “Maneuver” mode and use less than 300 s to achieve the target attitude of “Earth pointing”. The $y_{p}$ in the inertial frame is related to $x_{O}^{I}$ and it can be written as

y_{p}^{I} = \frac{z_{p}^{I} \times x_{O}^{I}}{| z_{p}^{I} \times x_{O}^{I} |}

(6)

where the vector

x_{O}^{I}

is the axis of orbit frame but described in inertial frame. If we want to calculate the attitude in inertial frame, the

x_{O}^{I}

can be written as

x_{O}^{I} = C_{O}^{I} x_{O}^{O}

(7)

The transform matrix $C_{O}^{I}$ , which is from orbit frame to inertial frame, can be calculated by the orbit extrapolation algorithm. And there is $x_{O}^{O} = {[\begin{matrix} 1, & 0, & 0 \end{matrix}]}^{T}$ .

According to the right hand rule, the $x_{p}$ can be defined by the cross product of $y_{p}$ and $z_{p}$ . It can be written in the inertial frame as

x_{p}^{I} = y_{p}^{I} \times z_{p}^{I}

(8)

After getting the three axes of the point frame, we can calculate the transform matrix as

C_{p}^{I} = [\begin{matrix} x_{p}^{I}, & y_{p}^{I}, & z_{p}^{I} \end{matrix}]

(9)

The transform matrix from inertial frame to pointing frame is $C_{I}^{p} = {(C_{p}^{I})}^{T}$ . In equation (4), the vector $r_{I D}^{I}$ is firstly calculated in the ECEF(earth-centered, earth-fixed frame) by the latitude, longitude and height, which can be written as⁶

r_{I D}^{E} = [\begin{matrix} (R_{T} + H_{T}) \cos Φ_{T} \cos Λ_{T} \\ (R_{T} + H_{T}) \cos Φ_{T} \sin Λ_{T} \\ [R_{T} (1 - e_{E}^{2}) + H_{T}] \sin Φ_{T} \end{matrix}]

(10)

where

Λ_{T}

is the geographical longitude,

Φ_{T}

is the geographical latitude,

H_{T}

is the height,

R_{T}

is defined as follows

R_{T} = \frac{R_{E}}{\sqrt{1 - e_{E}^{2} \sin^{2} Φ_{T}}}

(11)

where

R_{E} = 6378137 m

which is the radius of the earth.

e_{E} = \sqrt{1 - {(1 - f_{E})}^{2}}

is the eccentricity of the cross section of the reference ellipsoid. and

f_{E} = 1 / 298.2572

is the oblateness of the earth. The transform matrix from ECEF to inertial frame can be obtained by time from GPS. The

r_{I D}^{I}

can be written as

r_{I D}^{I} = C_{E}^{I} r_{I D}^{E}

(12)

The vector $r_{I O}^{I}$ is also easily obtained by GPS. Since the transform matrix $C_{p}^{I}$ is determined by the above equations, the target attitude quaternion is obtained. The target angular velocity can be deduced according to the attitude kinematics algorithm.

Observation angle analysis

The attitude pointing accuracy of satellite is ${0.1}^{\circ}$ and the orbit is SSO. Therefore the distance and angel is not ideal in the observation. The further the angle is from 90 degrees, the longer the distance is, and also the light intensity decreases. ${0.1}^{\circ}$ leads the distance on the ground can be calculated as

d = 547 * \tan 1 \circ = 0.9547 km

(13)

It is necessary to analyze the effect of elevation angle. The conclusion is shown in Table 3.

Table 3.

Effect of elevation angle.

Elevation angle (°)	90	85	80	75	70	65	60
Transmittance	0.60	0.59	0.59	0.58	0.58	0.57	0.56
Distance (km)	547	549	555	566	582	603	631
Central light intensity (10⁶ cd)	3.016	3.000	2.970	2.913	2.834	2.733	2.612
Central illumination (10^-⁶ lx)	6.0	5.8	5.7	5.3	4.8	4.3	3.6
Angle of 0 apparent magnitude ( $^{\circ}$ )	±2.1	±2.1	±2.0	±1.8	±1.6	±1.3	±1.2
Radius of 0 apparent magnitude (km)	20.0	20.0	19.4	17.8	15.0	13.5	13.0

In conclusion, the satellite can achieve 0 apparent magnitude within 13 km when the elevation angle is larger than 60°.

Design of flash time

According to the electrice power of the satellite, the time for flash is set to 2 minutes. Consider the time for observation and the viewing experience, the recommended length is 20 characters. A dot “.” vocalized as “dit”, and a dash “-” as “dah”. For example, the most often used code is “SOS”, which can be written as “…–-…”. The communication protocol of the satellite specifies the time for the “dit” and the “dah” as Table 4.

Table 4.

Time set for Morse code.

	Dot(.)	Dash(−)	Time between dot and dash	Time between letters
Time (ms)	400	1000	400	800

Observation results

The flash test has been conducted several times after the satellite launched into the space. The digital SLR camera is used to catch the flash in the sky at the place for observation. But a normal SLR camera always takes overexposed photos. For astrophotography enthusiasts, time-lapse photography is applied to obtain the artistic photos. But those photos cannot be used to analyze the light intensity of the flash.

The camera use for catching the flash of the satellite is PST-3 made by TY-SPACE, which is a micro star sensor. “Ladybeetle-1” also uses PST-3 in ADCS. This star sensor can expose 10 times per second. When it is applied in space, it can output the inertial quaternion. We use the star sensor to take photos during the flash and the algorithm which is applied in the star sensor. The figures after the process is shown below in Figure 5.

Figure 5.

Photo after process of star sensor (right: zoom).

The above photo was taken at 19th December 2018, and it was the first test of flash mission. During the two minutes of the flash, the change of elevation and distance is shown in Table 5. The above photo is taken after the middle time.

Table 5.

Change of elevation and distance.

Time	Beginning	Middle (Best)	End
Elevation (°)	48	74	47
Distance (km)	721	574	725

Where the decimal means the gray level of the star point in the photo, and the number of the star which has been captured is denoted as the integer of the photo. From the photo, we can obtain the X and Y position of the stars. According to the star catalogues, we can find the numbers of those stars and know the apparent magnitude as shown in Table 6.

Table 6.

Gray level and apparent magnitude analysis.

No.	X position	Y position	Gray level	Apparent magnitude
1	159.472727	628.172727	110	3.71
2	204.096386	99.5100402	249	2.83
3	267.028986	229.333333	138	3.84
4	686.606383	869.425532	94	3.73
5	654.206897	769.344828	58	4.45
6	893.840426	794.819149	94	4.06
7	854.170213	602.817629	329	1.91
8	936.851351	660.986486	74	4.65
9	973.936324	515.97974	691	2.1
10	937.517241	37.3706897	116	3.58
11	1216.7482	407.841727	139	3.37
12	44.8228237	397.572266	3584	(Ladybeetle-1)

Due to the linear relationship between gray level and light intensity, the above data can be used to compare the light intensity, and then estimate the apparent magnitude of the satellite. The first line in above table, the gray level is 110, and the apparent magnitude is 3.71. The apparent magnitude of the satellite can be written as

m_{L B 1} = - 2.5 \log_{10} (\frac{3584}{110}) + m_{N o .1} = -0 .0724

(14)

Equation (14) means that comparing with the No. 1 star in the photo, the apparent magnitude of the satellite is -0.0724. The data from Table 6 are all used to calculate the apparent magnitude, and the result is shown in Table 7.

Table 7.

Apparent magnitude in comparison with stars.

No.	Apparent magnitude	No.	Apparent magnitude
1	−0.0724	7	−0.6829
2	−0.0654	8	0.4372
3	0.3038	9	0.3128
4	−0.2231	10	−0.1448
5	−0.0274	11	−0.1584
6	0.1069	Mean	−0.0194

The mean of the calculated apparent magnitude is -0.0194. Then most bright apparent magnitude is -0.6829. The above results can prove that the design of the flash is correct. Figure 5 is the photo by the star sensor. According to the design of the flash mission, the photo taken with long exposure can show the Morse code as Figure 6.

Figure 6.

Photo taken with long exposure by SLR camera.

The above figure is taken by NIKON D850 on the 6th December 2019.

Conclusion

As of August 2020, the satellite completed more than 40 times of flash mission. This function of the “Ladybeetle 1” is open to the public. For astrophotography enthusiasts, the activities are more attractive. It is the first time that there is a satellite can send message in this way as shown in Figure 7.

Figure 7.

Photo taken on the World Autism Awareness Day 2019.

The photo above is taken on the 2nd April, 2019 which is the World Autism Awareness Day. The Morse code on the photo means “Hello, children of the stars”. This activity was launched to make the public care about the children with autism.

It is a romantic idea for engineers. In this paper, the whole system for this mission is introduced, including the light energy estimation, attitude pointing mode design and observation angle analysis. Then the observation results are given, which can verify the correctness of the design. The satellite can achieve 0 apparent magnitude in the mission. This project links satellite technology to popular science education, and realizes a visible and controllable satellite flash technology for the first time. Meanwhile, its successful implementation provides more reference for satellite application in the future. We believe that the priority of education is to arouse students’ interests in science and engineering. It is inevitable that engineering education may be complex and boring. “Ladybeetle-1” has the normal functions of a satellite, but also proves the most special function for education, as some astronomy fans feel so touched and excited when they see the satellite shining on the vault of heaven. The artificial star is so different from the remote stars and is sure to lighten their passion to explore science.⁷

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conﬂicts of interest with respect to the research, author- ship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors received financial support from Beijing Commsat Technology Development Co., Ltd for the research and authorship.

ORCID iDs

Xia Mu

Sihai Li

Zhenxing Zhang

Bin Xi

Mingguo Xiao

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