Category Archives: Problem Sets

Problem Sets published by the Faculty

Hamiltonian for WalMart wishing well

In case anyone is interested, this is what I get for the Hamiltonian of the ice sliding on the wishing well.hamiltonian

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Aperture Photometry Test Cases

Here is the image we will be using to check your aperture photometry code this evening:

ApPhotTest.FIT

The following test cases use an aperture radius of 3 pixels, an annulus inner radius of 6 pixels, and an outer radius of 10 pixels. Uncertainties are given not because you need to report them, but to indicate an acceptable range for your answers.

  • Object near: (x,y)=(313,371)
    • Centroid: (x,y)=(312.94,371.29)
    • Total counts in aperture: 19202
    • Avg. sky counts in annulus: 333.94
    • Signal: 9638.2 +/- 104.0
    • Inst. mag.: -9.96 +/- .01
  • Object near: (x,y)=(396,521)
    • Centroid: (x,y)=(396.15,520.92)
    • Total counts in aperture: 18848
    • Avg. sky counts in annulus: 332.68
    • Signal: 9318.8 +/- 104.5
    • Inst. mag.: -9.92 +/- .01
  • Object near: (x,y)=(230,432)
    • Centroid: (x,y)=(229.75,431.72)
    • Total counts in aperture: 10643
    • Avg. sky counts in annulus: 332.02
    • Signal: 1134.1 +/- 52.3
    • Inst. mag.: -7.64 +/- .05

Baby OD Test Cases

Self-Check 1:

Position [AU, equatorial]
[2.54076127, 0.84513781, 0.3806295]
Velocity [AU/day, equatorial]
[-0.003577, 0.00943291, 0.00429106]
****************************************
Semi-major axis (a) [AU], [km * 1000]
3.0                       448793.6121
Eccentricity (e)
0.1
Long. of Asc. Node (Omega) [deg], [rad]
4.0                   0.0698131700798
Inclination (i) [deg], [rad]
1.0                   0.0174532925199
Argument of Perihelion (omega; w) [deg], [rad]
5.0                   0.0872664625997
Mean Anomaly (M) [deg], [rad]
9.0                    0.157079632679
*************************************************************************

Self-Check 2:

Position [AU, equatorial]
[1.57, 0.0677, 0.253]
Velocity [AU/day, equatorial]
[-0.00169, 0.00985, 0.00145]
****************************************
Semi-major axis (a) [AU], [km * 1000]
1.09662428346           164052.657764
Eccentricity (e)
0.460315249446
Long. of Asc. Node (Omega) [deg], [rad]
212.790065382           3.71388725645
Inclination (i) [deg], [rad]
16.0459534852          0.280054719938
Arg. of Peri. (omega / w) [deg], [rad]
325.338401578            5.6782262907
Mean Anomaly (M) [deg], [rad]
196.414683647            3.4280829289
*************************************************************************

The TAs will have a third test case to test you against.

baby OD

If the baby is at ( 0, 0, 1.5 ) with the velocity ( 0.7, 0.7, 0 ), the orbital elements include I=90 deg, e=0.47, Omega=-135 deg (+360 deg, I guess), and omega=90 deg. I don’t know about a or M.

For what it is worth, for this year’s unfortunate baby, I get

a=2.7798, e=0.23435, I=12.028 deg, Omega=161.52 deg, omega=322.46 deg, M=327.60 deg.