Effects of Mars Rotation on Planet Imaging

Mars Rotation Image Smearing

Mars rotation needs to be taken account in how many images can be stacked. The benefit of stacking is that image noise is reduced when more images are stacked, but as more images are taken the greater the problem of image smearing is caused by Mars rotation. The trade off is reducing noise versus the effects of Mars rotation image smearing.

Mars image details are smeared across pixels if Mars rotates too much during the time span that all the images are taken. For example, image details are reduced in stacking if a pixel of the first image contains image detail that is different image detail in the last image as a result of Mars rotation. Details are smeared when the same pixels across different images contain different image details and these pixels are combined when the images are stacked.

Image smearing is dependent upon the arcseconds of planet movement from first to last image and the imaging equipment’s resolution in arcseconds of per pixel.

For example, the Nikon Coolpix 990 Digital Camera afocal coupled to a Tele Vue Radian 4mm eyepiece on an Orion Telescopes & Binoculars Argonaut™ 150mm Maksutov-Cassegrain telescope took the above Mars image on July 4, 2003. 72 images were taken over a six minutes time duration and stacked into one image. The above Mars image is 250 pixels in diameter and Mars was 17.24 arcseconds in diameter when the image was taken. Therefore, 17.24 arcseconds / 250 pixels = .069 arcseconds/pixel resolution for this imaging setup. Using the below table there was approximately 0.217 arcseconds of planet movement or about three pixels of planet movement at the center of Mars over the six minutes of images. Use the table column for six minutes time duration and use the row for Mars 17 arcseconds in diameter. At the center of Mars there is about three pixels of smearing caused by Mars rotation.

Table Details

The calculation the movement at the central meridian is dependent upon time duration and the size of Mars. The table below lists the approximate arcseconds of movement at the central meridian and equator depending upon the diameter of Mars in arcseconds and length of time in minutes. The diameter of Mars can be obtained from Mars software programs such as Mars Previewer II V2.01 or Meridian 4.8.

Approximate Arcseconds of Movement at the Center of Mars
Mars Diameter in Arcseconds	Time Duration in Minutes
	1 Min.	2 Min.	3 Min.	4 Min.	5 Min.	6 Min.	7 Min.	8 Min.	9 Min.	10 Min.
10	0.021	0.043	0.064	0.085	0.106	0.128	0.149	0.170	0.191	0.213
11	0.023	0.047	0.070	0.094	0.117	0.140	0.164	0.187	0.210	0.234
12	0.026	0.051	0.077	0.102	0.128	0.153	0.179	0.204	0.230	0.255
13	0.028	0.055	0.083	0.111	0.138	0.166	0.193	0.221	0.249	0.276
14	0.030	0.060	0.089	0.119	0.149	0.179	0.208	0.238	0.268	0.298
15	0.032	0.064	0.096	0.128	0.159	0.191	0.223	0.255	0.287	0.319
16	0.034	0.068	0.102	0.136	0.170	0.204	0.238	0.272	0.306	0.340
17	0.036	0.072	0.108	0.145	0.181	0.217	0.253	0.289	0.325	0.361
18	0.038	0.077	0.115	0.153	0.191	0.230	0.268	0.306	0.344	0.383
19	0.040	0.081	0.121	0.162	0.202	0.242	0.283	0.323	0.364	0.404
20	0.043	0.085	0.128	0.170	0.213	0.255	0.298	0.340	0.383	0.425
21	0.045	0.089	0.134	0.179	0.223	0.268	0.313	0.357	0.402	0.446
22	0.047	0.094	0.140	0.187	0.234	0.281	0.327	0.374	0.421	0.468
23	0.049	0.098	0.147	0.196	0.245	0.293	0.342	0.391	0.440	0.489
24	0.051	0.102	0.153	0.204	0.255	0.306	0.357	0.408	0.459	0.510
25	0.053	0.106	0.159	0.213	0.266	0.319	0.372	0.425	0.478	0.531

Table Formula

The above table makes some approximations that are not exactly correct, but are used to obtain some simple approximate values. For example, the table assumes the greatest amount of Mars movement is at the central meridian and equator. This assumption is only true when Mars’ axes of rotation is parallel with the Earth’s axes of rotation. The second assumption is using the Sin function to calculate the arcseconds of movement as seen from Earth. The Sin function produces a slightly larger value than the true value.

The formula use in the below table is arcseconds of planet movement as seen from Earth = (Mars radius in arc seconds as seen from Earth)*Sin(angle of Mars movement based on the total time duration of the images)

(Mars radius in arc seconds as seen from Earth) = (Mars diameter in arc seconds/2 as seen from Earth)

(Angle of Mars planet movement based on time duration of images) = (360 degrees/1477.4 minutes in a Mars day)*(time duration of images in minutes)*(pi/180)

Note: pi/180 converts degrees to radians for the Sin() function in Excel.

The Microsoft Excel .xls file worksheet used to calculate the above table.

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