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Getting Started Guide

Starting Your First Mission

Running the Mission

1.Spacecraft2

2.Spacecraft1

3.0.5 Days

Using Impulsive Burns

1.Spacecraft1 has a higher velocity right after the burn

2.Spacecraft1's variance in velocity increased

Orbital Elements Tutorial

Orbit Shapes and Sizes

Semi-Major Axis

1.Spacecraft1

2.Spacecraft3

3.Spacecraft3's period is approximately 24 hours

Eccentricity

1.Spacecraft3 and Spacecraft3

2.The peak in velocity occurred at the periapsis of the orbit

3.All of the Spacecrafts' periods are the same

4.The higher the eccentricity, the more variance in velocity

Orbit Orientation

Inclination

1.Spacecraft3

2.Spacecraft1

3.The Spacecraft travels in a retrograde orbit

Right Ascension of the Ascending Node (RAAN)

1.12 times

2.15 times

Argument of Perigee

1.Spacecraft4

2.The inclination needs to be 90 degrees, and the argument of perigee needs to be 270 degrees

True Anomaly

1.Approximately 100 minutes

2.Approximately 25 minutes

Spacecraft Attitude

Attitude State Representations

Euler Angles

1.Roll is a rotation about the spacecraft body X-axis, Pitch is a rotation about the spacecraft body Y-axis, Yaw is a rotation about the spacecraft body Z-axis

2.scYaw now has the same attitude motion as scRoll

Modeling the Direction Cosine Matrix and Quaternions

1.If hand calculations were correct, scEuler, scDCM, and scQuaternion were all set to the same attitude using different methods. Therefore, they should appear as one spacecraft

2.Rounding at 5 significant figures, answers should be well within 1% of actual values

3.At any given time, the components of the quaternion satisfy the constraint equation, and q4 never becomes a negative value

Attitude Reference Frames

LVLH vs Other Reference Frames

1.LVLH

2.MJ2000

3.At apogee and perigee

4.At any time the Flight Path Angle and the Euler Angle together equal 180 degrees, showing that the change in Pitch is equivalent to the Flight Path Angle

5.X-axes are always parallel, this is because the velocity vector on a circle is always tangent to the circle at any given time, making it the same vector as the Local Horizontal

Mission Constraints on Spacecraft Attitude

Custom Mission Attitude Frame

1.Minimum is approximately 1045W - Maximum is approximately 3495W - Yes this meets the requirements

2.scToSun defines the rotation about the primary scToCanberra Vector

3.No, our sensor points toward space and we do not receive enough power

Maneuvering Tutorial

Hohmann Transfer

Hohmann Transfer - Earth Centered

3.Answers should be within 1 m/s accuracy

4.Decrease

Bi-Elliptic Transfer

Modeling the Bi-Elliptic Transfer

4.Answers should be within 1 m/s accuracy

5.Δv1 = 2.952 km/s, Δv2 = 0.775 km/s, Δv3 = -0.301 km/s, ΣΔv = 4.029 km/s

6.The Hohmann transfer used 0.017 km/s more

7.Decrease

Phasing Maneuver

Modeling a Phasing Maneuver

1.Final output should look like this:

phasingOutput

Phasing Orbit

2.It used a total of 0.246 km/s less

Plane Change Maneuver

Modeling Plane Change Maneuvers

1.Answers should be within 1 m/s accuracy

2.Plane change maneuvers require less Δv for slower spacecraft

3.At the apoapsis of the intermediate transfer orbit

Interplanetary Topics

Interplanetary Hohmann Transfer

Modeling an Interplanetary Hohmann Transfer

1.5.596 km/s

2.259.32 days

3.Approximately 14.24 km

Patched Conics Transfer

Modeling a Patched Conics Transfer

1.Δv1 = 3.485 km/s, Δv2 = -2.254 km/s

2.ΣΔv = 5.739 km/s

3.280869.54 km

Gravity Assist

Modeling a Gravity Assist

1.BackSideSC

2.The Spacecraft exited in the same general direction as the Mars velocity vector

3.The magnitudes are within 0.040 km/s of each other. Their orbits are so drastically different because they had different exit directions in reference to the planet's velocity.

The B-Plane

Modeling the B-Plane

1.<9142.492, -4264.283, -3147.362> km

2.4.725 degrees

3.Answer should be within 1 meter

Targeting Tutorial

Inclination Change

Use Targeting to Model an Inclination Change

1.Calculations by hand should match with FreeFlyer's calculations. You can solve for the initial velocity using the circular velocity formula. Solutions:

•Δvnv: 1.1417 km/s - notice that FreeFlyer represents this as negative, because it is opposite the velocity direction

•Δvn: 3.6213 km/s

•Total Δv: 3.797 km/s

2.Achieving goals for SMA and eccentricity instead of circular velocity should yield the same results.

3.Coming from a non-equatorial orbit would require the burn to be performed at either the ascending or descending node. We would need to step our spacecraft to one of these positions in its orbit before executing the targeting loop in order to achieve a proper inclination change.

4.The Targeting loop in FreeForm script should look like this:

Target;

Iterate Spacecraft1;

// Elements we can vary to achieve the desired inclination

Vary ImpulsiveBurn1.BurnDirection[0] = 0 + 0.001;

Vary ImpulsiveBurn1.BurnDirection[1] = 1 + 0.001;

// Perform the maneuver

Maneuver Spacecraft1 using ImpulsiveBurn1;

// Goals to achieve with the maneuver

Achieve Spacecraft1.I = 35 +/- 0.01;

Achieve Spacecraft1.VMag = initialVelocity +/- 0.001;

End;

B-Plane Targeting

Targeting Mars's B-Plane

1.Angle between B and T: 114.923 degrees. B magnitude: 8004.149 km. Both are within their respective tolerances.

2.We only burn in the V direction because our B-plane targeting means we are already in the correct plane to achieve a polar orbit. We just need to slow down so that we do not fly by Mars. If we allow the other two burn directions to vary, their magnitudes are negligible.

Real World Modeling