MAE 2201 FA13 Lecture 24 Orbital Eq

8/10/2019 MAE 2201 FA13 Lecture 24 Orbital Eq

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Rockets-Micro thrusters

State of the artmicrothrusters…

DARPA + Tanner

research

Micro-thrusters are

miniature actuators…




Micro-thrusters are miniature actuators created using smallcavities, rocket propellant, and low energy igniters.

Work like Space Shuttle solid boosters, but are 1000’s of times smaller

Individual micro-electromechanical system (MEMS) thrusters

size: poppy seed-sized cell fueled with lead styphnate propellant, fired

more than 20 times at 1-second intervals each thruster delivered 0.0001 Newton seconds of impulse.

MEMS design, based on silicon chip fabrication technology, offers

several advantages over conventional thrusters

no moving parts

utilizes a variety of propellants

is scalable

eliminates the need for tanks, fuel lines and valves, and fully

integrates the structure of the satellite with the propulsion to power it.




MEMS micro-thruster arrays are fabricated as a three-layersilicon and glass sandwich,

middle layer consisting of multiple small propellant cells sealed with

a rupturable diaphragm on one side and an ignitor on the other.

Each cell is a separate thruster, and when ignited, delivers one

impulse bit.

Delivering propulsion in discrete increments by igniting thrusters in

controlled sequences has lent the technology the name "digital

propulsion."




State of art Cavity now built of aluminum to withstand higher pressures

Cavity is 4mm per side

Latest micro-thruster design may generate up to 40 mN-seconds of

impulse by combusting 35 milligrams of propellant primarily composed

of black powder.

Isp=116 s

Will be used for small satellites, guided munitions etc.



Orbital Mechanics

Last time we discussed burnout velocity…why isthat important?

Velocities on order of 7.9 km/s are needed to place

satellites in Earth orbit

Interplanetary vehicles need 11 km/s to get out of Earth’s

gravity











Orbital Mechanics

Starts with Kepler who developed the three laws of planetarymotion

First: The orbit of each planet is an ellipse, with the sun at

a focus

Second: The line joining the planet to the sun sweeps out

equal areas in equal times



Parameters of Elliptic Orbit



Orbital Mechanics

Third: The square of the period, (time for 1 orbit) of aplanet is proportional to the cube of its mean distance

from the sun (semi-major axis, “a”, of the ellipse)

Review Example Problem 8.2 on pg. 675 for period

calculations

Newton:

Law of gravity:

r mma F

r

r

r

GMm F

2



Orbital Mechanics

Law of gravity: G is gravitational constant

Vector r is distance

M, m are masses of the two bodies

The potential energy of a body of mass m foundsome distance away from a body of mass M (>m) is:

The kinetic energy of the small body is (in a polarcoordinate system):

r

r

r

GMm

F

2

r

GMm

222

2

1

2

1 r r mmV T



Orbital Mechanics

The motion of the space vehicle in the direction is the conservation ofangular momentum

The orbit equation : gives the orbital or trajectory motion of satellite or planet

e eccentricity e=0; path is circle

e<1; path is an ellipse

e>1; path is hyperbola

e=1; path is parabola

h is angular momentum per unit mass is a constant =

p=h2 /k2 e=A(h2 /k2) all these are determined from burnout conditions

G*M=k2

Review Example Problem 8.1 on page 668 for trajectory calculations

I momentumangular

const r m

_

.2

)cos(1 C e pr

2r



Orbital Mechanics

e eccentricity e=0; path is circle

e<1; path is an ellipse

e>1; path is hyperbola

e=1; path is parabola

e

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MAE 2201 FA13 Lecture 24 Orbital Eq