Colorado Space Grant Consortium

Gateway To SpaceASEN / ASTR 2500

Class #15

Colorado Space Grant Consortium

Gateway To SpaceASEN 1400 / ASTR 2500

Class #19

T-32

- Announcements

- Mid Semester Team Evaluations

- Orbits and Mission Design – Part I

- Launch is in 32 days

Today:

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Announcements…

Grades - Don’t panic

Spider?

DD Rev A/B Comments-Mission sections should read like a science paper- Cooler test should be fully functional + Dry Ice Bombs- Mission Statements + RFP- Requirement Section – Team #1 - Testing Section – Team #4 - Hardware Section – Team #6

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Mid Semester Team Evaluations…

- Due at the start of class on Thursday- Team of six has 1200 points

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Total = 1200 points

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Mid Semester Team Evaluations…

- Say not everyone is pulling their weight

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Total = 1200 points

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Mid Semester Team Evaluations…

- I take everyone’s scores and do the math, taking into account how self scoring compares to team score for you

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Colorado Space Grant Consortium

Thursday…Orbits and Mission Design – PART II

Mid Semester Team Evaluations due in class

30 days to launch

Colorado Space Grant Consortium

Next Tuesday…Guest Lecture on ADCS

Colorado Space Grant Consortium

Orbits and Mission Design – Part 1ASEN 1400 / ASTR 2500

Class #19

Orbits:A Brief Historical Look

Earth, the Moon, Mars, and the Stars Beyond

A Brief Discussion on Mission Design

Questions:

• How fast can you throw a snowball? - A baseball? - A shot put?

- A Subway sandwich out a moving car?

• Could you throw any of these in to an orbit? - How fast would it have to be going?

Universal Gravitation, Applied:

• What is an orbit?

Questions:

• Let’s figure it out…

v GM

R

G 6.67x 10 11 m3

kg s2

MEarth 5.974x 10 24 kg REarth 6367000 m

MMoon 7.350x 10 22 kg RMoon 1738000 m

v is velocityG is Universal Gravitational ConstantM is mass of planet or satelliteR is radius of planet of satellite

v Earth 7910 ms 17694 mph

v Moon 1679 ms 3756 mph

Universal Gravitation, Applied:

• When in space why do you float? i.e. Weightlessness

r

MGV

r

MmG

r

mV

2

2

Orbit History:

• 1665 A.D. Isaac Newton

• At 23, plague while at Cambridge

• Went to be one with nature• He studied gravity• Discovered “Newton’s Laws of

Motion”• 1666, he understood planetary

motion• Did zip for 20 years until

Edmund Halley

Newton’s Laws:

1st Law.....Body at rest stays at rest, a body in motion

stay in motion

2nd Law....F = m * a

3rd Law...For every action, there is an equal and opposite reaction

Newton’s Laws:

Newton Continued... • 1687, Principia Published• Law of Universal Gravitation (Attraction)

221

r

GmmF

Newton’s Laws:

Newton Continued... • 1687, Principia Published• Law of Universal Gravitation (Attraction)

221

r

GmmF

r

VmF

22ma

Universal Gravitation, Applied:

• When in space why do you float? i.e. Weightlessness

r

MGV

r

MmG

r

mV

2

2

Questions:

• Let’s figure it out…

v GM

R

G 6.67x 10 11 m3

kg s2

MEarth 5.974x 10 24 kg REarth 6367000 m

MMoon 7.350x 10 22 kg RMoon 1738000 m

v is velocityG is Universal Gravitational ConstantM is mass of planet or satelliteR is radius of planet of satellite

v Earth 7910 ms 17694 mph

v Moon 1679 ms 3756 mph

Atmosphere:

• How about throwing something into orbit on the moon?

golf ball

Atmosphere:

• Let’s figure it out…

v GM

R

v is velocityG is Universal Gravitational ConstantM is mass of planet or satelliteR is radius of planet of satellite

v Earth 7910 ms 17694 mph

v Moon 1679 ms 3756 mph

G 6.67x 10 11 m3

kg s2

MEarth 5.974x 10 24 kg REarth 6367000 m

MMoon 7.350x 1022 kg RMoon 1738000 m

v Earth 7910 ms 17694 mph

v Moon 1679 ms 3756 mph

Orbits:A Brief Historical Look

Arthur C. Clarke

Discovered This Orbit

Ancient Orbit History:

“ORBIT” from Latin word “orbita” orbitus = circular; orbis = orb

• 1800 B.C. Stonehenge

- Study of the vernal equinox

1500 B.C.: Egyptians and Babylonians

• Written evidence of stellar observations

• Solar Calendar of 365 days

• Time divided into 60 even units

Aristotle• Said earth is center of the universe• Dominated scientific thought for

1800 years

350 B.C.: Greek Thoughts

Start of the Heliocentric Model:

1543 A.D. Nicholas Copernicus

• Said Sun-centered rotations

• Measurements crude but thinking shifts

• Didn’t release findings until the end of his life

Orbit History :

• 1580 A.D. Tycho Brahe

• Accurate measurements of planets (Mars) as a function of time

• Even though telescope had not been invented

Orbit History :

• 1610 A.D. Galileo Galilei

• Good friends with Copernicus

• Observations with TELESCOPE reinforced

• Discovered Venus has phases

Orbit History:

• 1600 A.D. Johannes Kepler

• Used Tycho’s careful Mars observations to smash

Aristotle theories• Presented 3 laws of planetary

motion• Basis of understanding of

spacecraft motion• However, “Why was not

understood”• Calculus?

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One Minute Report…

-

Gottfried Leibniz Isaac Newton

Orbit History:

Kepler’s 3 Laws of Planetary Motion:

1. All planets move in elliptical orbits, sun at one focus

Orbit History:

Kepler’s 3 Laws of Planetary Motion:

1. All planets move in elliptical orbits, sun at one focus

Orbit History:

Kepler’s 3 Laws of Planetary Motion:2. A line joining any planet to the sun, sweeps

out equal areas in equal times

Orbit History:

Kepler’s 3 Laws of Planetary Motion:2. A line joining any planet to the sun, sweeps

out equal areas in equal times

Orbit History:

Kepler’s 3 Laws of Planetary Motion:3. The square of the period of any planet about the sun is

proportional to the cube of the of the planet’s mean distance from the sun.

If you can observe the period of rotation, you can determine the distance

Planet P (yr) a (AU) T2 R3

Mercury 0.24 0.39 0.06 0.06

Venus 0.62 0.72 0.39 0.37

Earth 1.00 1.00 1.00 1.00

Mars 1.88 1.52 3.53 3.51

Jupiter 11.9 5.20 142 141

Saturn 29.5 9.54 870 868

T2 = R3

Types of Orbits:

Orbits are conic sections:• Circle• Ellipse• Parabola• Hyperbola

From Kepler’s Law, the central body is at a focus of the conic section

a

MG

r

MGV

2

Kepler:

Kepler’s Laws...Orbits described by conic sections

Velocity of an orbit described by following equation

For a circle (a=r):

For a ellipse (a>0):

For a parabola (a=):

v2 r

a

GM

v r

v2 r

a

v2 r

Questions:

• Let’s figure it out…

v GM

R

G 6.67x 10 11 m3

kg s2

MEarth 5.974x 10 24 kg REarth 6367000 m

MMoon 7.350x 10 22 kg RMoon 1738000 m

v is velocityG is Universal Gravitational ConstantM is mass of planet or satelliteR is radius of planet of satellite

v Earth 7910 ms 17694 mph

v Moon 1679 ms 3756 mph

Earth, the Moon, Mars, and the Stars Beyond

A Brief Discussion on Mission Design

Orbit Introduction:

What is an orbit?- The path of a satellite around the Earth (or any central body)

What shape is it?- Orbits are conic sections- Circles, Ellipses, Parabolas, Hyperbolas

How are orbits described?- Position and Velocity at any one time- Keplerian Elements (from Kepler’s Laws)

Orbit Definition:

Velocity & Position

- Given position and velocity of a satellite at time t, you can calculate the position and velocity at any other time

Orbit Definition:

Keplerian Elements

- Semi major axis (a)- Size

- Eccentricity (e)- Shape

Orbit Definition:

Keplerian Elements

- Inclination (i)- Angle to the Equator

Orbit Definition:

Orbit Definition:

Keplerian Elements

- Right Ascension of Ascending Node (RAAN, Ω)- Rotation about the Earth’s Spin Axis

Orbit Definition:

Keplerian Elements

- Argument of Perigee (ω)- Rotation of the conic section in the plane

Orbit Definition:

Keplerian Elements

- True Anomaly (θ)- Defines the position of a body in orbit- Angle between the Position Vector and the vector to Perigee- Elliptical only

Orbital Elements:

• Used to determine a satellite’s location in orbit:

Types of Orbits:

Types of Orbits:

Types of Orbits (cont.)

• Geosynchronous/Geostationary (equator)

Types of Orbits (cont.)

• Critical Inclination

Types of Orbits (cont.)

• Repeating Ground Trace

• Polar/ Sun Synchronous

Types of Orbits (cont.)

Types of Orbits (cont.)

• Molniya