Orbit Design of Cube Satellite

Orbit Design of Cube Satellite Moutaman Mirghani1, Hoyam Abobaker2, Eshraga Adel3, Asia Saeed Kajo4 Institute of Space Research and Aerospace (ISRA), Khartoum, Sudan 1 [email protected], [email protected], [email protected], [email protected] Abstract—the process of locating and putting satellites in a specific orbit is one of the complicated processes in satellite design, comparing small satellites to the large space. It depends on various parameters called Keplerian elements, such as orbital inclination, mean motion, mean anomaly, eccentricity, and argument of perigee and right ascension of ascending node. The actual geometric or physical meaning of these parameters of the orbit will depend upon the method of approach used in solving the Kepler equation. Determining this parameters accurately is significant on building satellite system that guarantees optimal performance of the mission which it was launched for. On this paper the format of two line element is explained and the parameters of orbit are determined by using orbit simulation software. Keywords—orbit, Keplerian element, two line element format.

I.

INTRODUCTION

Satellite orbit is a path that the satellite must follow to be able to turn around the Earth. There are many different factors that orbit can be classified according to it. The basic classification of the orbit is altitude classification, which includes Low Earth Orbit (LEO), Medium Earth Orbit (MEO) and Highly Elliptical Orbit (HEO). The orbit is chosen according to satellite mission or application that is designed for. For example, those satellites used for direct television broadcast and other communications satellites use Geostationary Orbits (GEO). Other satellite systems such as phone network satellites may use Low Earth orbiting systems. On the other hand, satellite systems used for navigation, like Navistar or Global Positioning System (GPS), occupy a relatively higher Earth orbit such as MEO. The process of designing orbit is very important process depending on many parameters and accurate calculation. This paper focuses on how to select and design the LEO orbit for ISRASAT1 cube satellite. II.

LAWS DESCRIBE THE MOTION OF SATELLITE IN ORBIT

Gravity is one of the four fundamental forces in nature. It is invisible force of attraction between any two objects in the universe, which is not only valid on falling objects but also for orbiting object planets or satellites. Newton’s law of universal gravitation stated that; between any two masses in the universe there is a force of attraction between them, which is directly proportional to the product of their masses, and inversely proportional to the square of the distance separating them [1]. Mathematically, 𝑓=

Gm 1 m 2 𝑟2

)1(

Where 𝑓 m1 , m2 𝐺 𝑟

Attraction force Objects masses. Constant of gravitational. Distance between objects.

Explaining the motion of celestial bodies, especially the planets, has challenged observers for many centuries started by the Greeks and Nicolaus. Finally, with the help of Tycho Brahe's observational data, Johannes Kepleron (1571-1630) was able to derive empirically three laws describing planetary motion, which are as follows. A. Kepler’sFrst Law States that the orbit of each planet is an ellipse with the Sun at one focus. [2] B. Kepler’Second Law States that the speed of planet varies in such a way that the line joining the planet and the Sun sweeps out equal areas in equal times. [3] C. Kepler’s Third Law States that the square of the periodic time of orbit is proportional to the cube of the mean distance between the two bodies. The mean distance is equal to the semi major axis [2]. The mathematical relation is 4π 2 r 3

T2 =

Gm

)2(

Where 𝑇 𝐺𝑚 𝑟

Periodic time of the satellite. Constant (µ= 3.9*1014 m3/sec2). Distance between satellite and earth.

Isaac Newton (1642-1727) was able to derive Kepler’s laws from his own laws of mechanics and gravitantial, considered the motion of a planet around the Sun. In a circular orbit, there must be centripetal force acting on the planet to force it into the circular motion (that is the same of the motion of satellite around the Earth). This centripetal force acting on the satellite is supplied by the force of gravity of the earth its equation shown below. Fc =

mv 2 r

)3(

Where Fc Centripetal force 𝑚 Mass of the earth

The 10th Scientific Conference of National Center for Research, Khartoum, 1-3 Dec 2015.

Page 1

𝑣 𝑟

Velocity of the satellite Distance between center of Earth and satellite.

Because the centripetal force is supplied by the gravitational force, we have

Fcentripetal = Fgravitational 𝑚 1 𝑣2

𝐺𝑚 1 𝑚 2

=

𝑟

𝑟2

(4)

Then 𝑣2 =

𝐺𝑚 2

(5)

𝑟

Figure1 Coinic Section of Orbit [4]. Where 𝑣=

2𝜋𝑟

(6)

𝑇

By substitute on the above equation we reach to Kepler third law relation is: T2 = III.

4𝜋 2 𝑟 3 𝐺𝑚

(7)

KEPLERIAN ELEMENTS

There are several Kepler elements that describe the orbit of a satellite, such as: A. Eccentricity (e) Is the element used to determine the shape of orbit and tells how flat the orbit is. Depending on e, we get [1] If (e=0)

the orbit will be circular

(0