Sea Launch/Zenit

Thrust:8,180,000 N

Fueled Weight:450,000 kg

Payload to LEO:13,740 kg

Cost per launch:

$100,000,000Cost per kg:

$7,300Launches:

31/28

Present:

Colorado Space Grant Consortium

Gateway To SpaceASEN 1400 / ASTR 2500

Class #20

T-30

- Announcements

- One minute Report Questions

- Mid Semester Team Evaluations

- Orbits and Mission Design – Part II

- Launch is in 30 days

Today:

4

Announcements…

pCDR peer reviews…- 3rd place is Team #5- 2nd place is Team #7- 1st place is Team #4

DD Rev A/B Grades

HW #8 Due 4:00 PM November 9th

Office Hours and Questions in Class

5

Mid Semester Team Evaluations…

Please pass them forward now

New grades posted next Tuesday

Community Service project will be included

Colorado Space Grant Consortium

Next Tuesday…Guest Lecture on ADCS

One Minute Reports:

Geostationary VS. Geosynchronous

One Minute Reports:

- What types of orbits do they do around other planets?

- Is there a polar orbit that is also geosynchronous?- Could spacecraft ever be launched from Colorado?- How do you get on elliptical orbit? - What is the advantage of elliptical orbit vs. a circular

orbit around the Earth?- Does the angle at which you launch a satellite affect

its eccentricity?- How many different orbits are there?- Do you have launch a satellite at an angle to get it

into orbit or can you shoot it straight up?

Types of Rockets:

One Minute Reports:

- Who owns the geosync orbit space? UN through the International Telecommunications Union

- When is our Movie Night?- What is the amount of time between turning on the

Sat at launch?- Do you have to write a journal about every chapter?- How will the in-class simulation work?- Do we need to have all the satellite building and

testing done before the in-class simulation?- What chances do students have to go to those big

conferences?

-

One Minute Reports:

- Where does Tom Kelly work now?

One Minute Reports:

-- What is an acoustic test?- Are vibration tests done with mass models or the

actual products?- Did they use Velcro on floor to keep them in place?- Has an emergency ever occurred on an EVA?- Is Grumman still making space vehicles?- Arduino is beginning to look like a next of wires?- Why is water blue?- Why is this class so awesome?

- What is the craziest thing I ever did…

Colorado Space Grant Consortium

Orbits and Mission Design – Part 2ASEN 1400 / ASTR 2500

Class #19

Orbits:A Brief Historical Look

Earth, the Moon, Mars, and the Stars Beyond

A Brief Discussion on Mission Design

Universal Gravitation, Applied:

• What is an orbit?

Newton’s Laws:

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

221

rGmmF

rVmF

22ma

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: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 0.37Earth 1.00 1.00 1.00 1.00Mars 1.88 1.52 3.53 3.51

Jupiter 11.9 5.20 142 141Saturn 29.5 9.54 870 868

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

aMG

rMGV

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

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

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

Circular Orbit:

For a 250 km circular Earth Orbit

Orbital Velocity

v r

v398600.4

(250 6378.14)

v7.75 kmsec

17,347 mph

Circular Orbit:

Orbital Period

Circular Orbit:

For a 500 km circular Earth Orbit

Orbital Velocity

v r

v398600.4

(500 6378.14)

v7.61 kmsec

17,028 mph

Circular Orbit:

For a 500 km circular Earth Orbit

Orbital Period

Conclusions???

P 2 r3

P 2(500 6378.14)3

398600.4P 5,676 sec 94.6 min

Changing Orbits:

How about 250 km to 500 km

How would you do it?

Changing Orbits:

Changing orbits usually involves an elliptical orbit or Transfer Orbit

Perigee = closeApogee = far

apof

iper

vvv

vvv

2

1

Changing Orbits:

1) Velocity of initial orbit

2) Velocity of final orbit

3) Velocity at perigee 4) Velocity at apogee

v f 7.61 kmsec

apof

iper

vvv

vvv

2

1

Changing Orbits:

Since orbit is elliptical at Vper and Vapo a > 0, so

where

v2 r

a

a r1 r2

2

a (250 6378.14) (500 6378.14)

2a 6753 km

Changing Orbits:

So back to our V’s3) Velocity at perigee

vper 2 r

a

vper 2* 398600.4

(250 6378.14)

398600.46753

vper 7.83 kmsec

Changing Orbits:

So back to our V’s4) Velocity at apogee

Changing Orbits:

1) Velocity of initial orbit

2) Velocity of final orbit

3) Velocity at perigee 4) Velocity at apogee

v f 7.61 kmsec

apof

iper

vvv

vvv

2

1

vapo 7.54 kmsec

Changing Orbits:

Therefore:V1 is to start transfer

v2v1

Changing Orbits:

V2 is to circularize orbit

v2v1

Changing Orbits:

What if we did the whole thing in reverse?

Go from 500 to 250 km?

What happens to the answer?

Changing Orbits:

1) Velocity of initial orbit

2) Velocity of final orbit

3) Velocity at perigee 4) Velocity at apogee

vapo 7.54 kmsec

Changing Orbits:

Therefore:V1 is to start transfer

Changing Orbits:

V2 is to circularize orbit

Changing Orbits:

Time to do transfer is the same

v2v1

How well do you understand Hohmann Transfers?

123

• 1 to 2?

• 2 to 3?

• 3 to 1?

• 1 to 3?

Circular Orbit:

Changing Orbits:

Also something called “Fast Transfer”

• It is more direct and quicker

• However it takes more fuel

• V1 and V2 are

much bigger