L1 - Introduction to Orbit Mechanics

Question 1

What is Kepler’s first law?

Answer 1

The orbits of the planets are ellipses with the Sun at one focus.

Question 2

What is Kepler’s second law?

Answer 2

The line joining a planet to the Sun sweeps out equal areas in equal times.

For same T, A1=A2.

Question 3

What is Kepler’s third law?

Answer 3

The square of the orbital period is directly proportional to the cube of the mean distance between the sun and the planet.

T² = a³

Question 4

State Newton’s law of gravitation.

Answer 4

Any two bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Question 5

What are the two-body problem assumptions?

Answer 5

• Two bodies
• Constant mass
• Exactly spherical
• Small body trajectory will be conic section: circle, ellipse, parabola or hyperbola

Question 6

Describe the geocentric equatorial (ECI) coordinate system.

Answer 6

• Origin - centre of Earth
• Fundamental plane - Earth’s equator
• Perpendicular plane - North Pole direction
• Principal direction - vernal equinox/first point of Aries direction
• Third axis - found with right-hand rule

Question 7

What is the vernal equinox/first point of Aries (FPA)?

Answer 7

It is the point in the sky at chich the sun appears on the first day of spring (March 21st). The FPA moves 1° every 70 years.

Question 8

What are the different types of orbit possible?

Answer 8

• Circle: e = 0
• Ellipse: 0 < e > 1
• Parabola: e = 1 (escape velocity)
• Hyperbola: e > 1 (escape trajectory)

Question 9

What is the eccentricity e?

Answer 9

It is a measure of how non-circular the orbit/trajectory is.

Question 10

What is the minimum inclination that can be achieved by a launched satellite?

Answer 10

That equal to the latitude of the launch site.

Question 11

What restriction is determined by the latitude of the launch site?

Answer 11

The latitude of a launch site is equal to the minimum achieveable inclination.

Question 12

What are the Classical Orbital Elements? (COE)

Answer 12

• a: Semi-major axis
• e: Eccentricity
• y: True anomaly
• I: Inclination
• Ω: Right Ascension of ascending node
• ω: Argument of Perigee

Question 13

What elements describe the size, shape and position of an orbit and satellite upon it?

Answer 13

• a: Orbit size
• e: Orbit shape
• y: Position of satellite on orbit

Question 14

Sketch a Keplerian orbit diagram.

Answer 14

Question 15

What is the inclination of an orbit?

Answer 15

It is the angle between the orbital plane and the reference plane (equatorial for Earth).

0 < I > 90 : Sat moves in Earth rotation’s direction

90 < I > 180 : Sat moves opposite to Earth Rotation

Question 16

What is the ascending node?

Answer 16

Ω is the point where a satellite passes through the equatorial plane from the southern hemisphere to the northern one.

Question 17

What is the Argument of Perigee?

Answer 17

ω is a measure of the angle in the orbit plane between the ascending node and perigee, measured in the direction travelled by the satellite.

Question 18

Draw an orbit diagram to define the ascending node and argument at perigee.

Answer 18