Orbiting

Question 1

Describe the existing satellite missions. Indicate types of orbit most preferable for the given
mission.

Answer 1

1. Earth Observation Satellites: monitor and study the Earth’s surface, oceans, and atmosphere. These satellites typically orbit in a low earth orbit (LEO)
2. Communication Satellites: relay voice and data signals from one point on the Earth’s surface to another. These satellites typically orbit in geosynchronous orbits (GEO)
3. Navigation Satellites: Navigation satellites are used to provide location and timing information for navigation systems such as GPS. These satellites typically orbit in medium earth orbits (MEO)
4. Weather Satellites: Weather satellites are used to monitor and study weather patterns. These satellites typically orbit in a polar orbit (PO)

Question 2

Describe Geocentric equatorial inertial (GEI) coordinates

Answer 2

The Geocentric Equatorial Inertial System (GEI) fixed relative to the stars. Its X- and Y-axes lie in the Earth’s equatorial plane and the Earth spins about the Z-axis. The X-axis is in a direction from Earth to the Sun at the vernal equinox (21 March). The direction thus indicated is termed the first point of Aries Υ. Its X-axis is pointing from the Earth towards the first point of Aries. This direction is the intersection of the Earth’s equatorial plane and the ecliptic plane. The Z-axis is along the Earth’s spin axis, in the northerly direction, i.e. at an angle ~23o to the normal of the ecliptic plane.

Question 3

what is the length of time of a sidereal day

Answer 3

23:56:04
86164.1s

Question 4

List of the parameters which are necessary to determine special position of a satellite in the Cartesian Geographic (CGeo).

Answer 4

1. Longitude of ascending node: Ω.
2. Orbit inclination: 𝑖.
3. Argument of periapsis: 𝜔
4. Perigee altitude: ℎ𝑝 (or orbit semi-major axis, or the orbit period)
5. Orbit eccentricity: 𝑒
6. Time referenced after the last passing of the perigee: 𝑡−𝑡𝑝
7. The side real time ST.

Question 5

Explain the difference between the solar day and the sidereal day

Answer 5

The solar day is the time it takes for the sun to return to its highest point in the sky, which is usually around 24 hours.
A sidereal day is the time it takes for an object in the sky, such as a star, to return to its highest point in the sky.

Question 6

Describe which forces should be balanced in a Lagrangian point.

Answer 6

the gravitational forces of two large bodies must be balanced
centrifugal force

Question 7

Describe how the Earth’s oblateness disturbs satellite orbit motion and explain why the inclination angle of 63.4 Degrees is the most appropriate for high elliptic orbits.

Answer 7

(a) in rotation of the line of nodes.

(b) in an overall rotation of the orbit within the orbit plane, i.e. in procession of the line of apsides.

The direction of this rotation depends on the orbit inclination.

The inclination angle of 63.4 degrees is the most appropriate for high elliptic orbits because it reduces the effects of precession on the satellite’s orbit. At this angle, the satellite’s orbit plane is perpendicular to the Earth’s axis of rotation. This means that the gravitational force acting on the satellite is even and does not cause the precession effect, allowing the satellite to remain in its initial orbital trajectory.

Question 8

Describe factors disturbing the satellite orbit from that described in the framework of two body motion. Which factors dominate at different attitudes?

Answer 8

The factors that disturb the satellite orbit from the two body motion framework include non-gravitational forces, atmospheric drag, solar radiation pressure, and the Earth’s oblateness.

At lower altitudes, atmospheric drag and solar radiation pressure are more dominant,

while at higher altitudes, the Earth’s oblateness is more dominant.

Question 9

Explain the meaning of terms: (ii) the eccentric anomaly,

Answer 9

a measure of the position of an orbiting body in its orbit as measured from a point called the center of the orbit.

Question 10

Explain the meaning of terms: (i) the true anomaly,

Answer 10

the angle between the angle of apsides and direction to the satellite from the focus

Question 11

Explain the meaning of terms: (iii) the mean
anomaly,

Answer 11

a measure of the angular distance of an orbiting body from its periapsis along its orbit

Question 12

Explain the meaning of terms:(iv) the mean motion.

Answer 12

average angular speed of an orbiting body with respect to the primary body around which it is orbiting.

Question 13

Explain the meaning of terms: (i) line of nodes,

Answer 13

the point where the orbital plane intersect the equatorial plane

Question 14

Explain the meaning of terms: (ii) ascending node,

Answer 14

the point where an object in orbit around a planet or other celestial body passes through the plane of reference

Question 15

Explain the meaning of terms: (iii) right ascension of this node,

Answer 15

is the angular distance, from a specified primary direction to the line of nodes

Question 16

Explain the meaning of terms: (iv) inclination angle,

Answer 16

Inclination angle is the angle between an object’s rotational axis and a reference plane.

Question 17

Explain the meaning of terms: (v) argument of periapsis.

Answer 17

The argument of periapsis is the angle from the body’s ascending node to its periapsis, measured in the direction of motion.

Question 18

what are Kepler’s 3 laws

Answer 18

1 - the orbit of every planet is an ellipse with the sun at one of the two foci
2 - a line joining a planet sweeps out equal areas during equal intervals of time
3 - the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit

Question 19

what are the parameters of eccentricity for keplar’s orbits

Answer 19

e = 0 circular orbit
0<e<1 elliptic orbit
e=1 parablic orbit
e>1 hyperbolic orbit

Question 20

what is the difference between the GSO and GEO

Answer 20

Period of the both GSO and GEO is exactly the sidereal day.
GSO can be elliptic and have any inclination.
GEO is strictly circular and equatorial that allows the satellite to have a fixed
position in the sky to ground observers.

Question 21

explain the Lagrangian point in the system of two orbiting bodies and how these can be used in satellite missions

Answer 21

Lagrangian points are positions in an orbital configuration of two large bodies where a small object can maintain a stable position relative to the two large bodies.

In these points the combined gravitational force of the two large bodies is balanced by the centripetal force required to orbit with them.

There are five such points, labelled L1 to L5. Points L1,L2,L3 are on the line connecting the two large bodies. Each of points, L4,L5, forms an equilateral triangle with the two large bodies.

Only points L4,L5 are stable: small perturbation of position and velocity will cause small periodic motion in the vicinity of the point.