Purpose: to become familiar with the image analysis program and to develop an understanding to the size and age of planetary nebulaeProcedureThe first part of the experiment involved using a picture of a church and back round to understand different pixels, ADU, zoom, and how to get the (x, y) coordinates. We then took this brief understanding of pictures and applied it to the stars. We loaded a picture of nebulae m 42. After this we needed to calculate the average number of stars or solar masses. We found the (x, y) coordinates of a position in the center of the nebulae and on the edge of the nebulae.

We used the following distance formula to find the distance between the points. After this calculation the answer in pixels needed to be converted to arc seconds for use in the small angle formula where 1 pixel approx. = 3 arc seconds. We now could use the small angle formula to find the actual radius in pc.

Where d is the radius D is the distance from the Earth in pc and theta is the value we had just found out in arc seconds. After the calculation we needed to convert pc to meters so we used the calculation factor of 1 pc = 3 10^16 m Now we needed to find the density. Density was figured out by multiplying the majority substance in the nebulae (hydrogen) per cubic m^3 by the mass of hydrogen in kg, which gave us the formula We then had the info we needed to find the mass of the nebulae. We calculated this by using a spherical shape for ease of calculation. We used the following formula where m is the mass p is the density and r is the radius found above from the small angle formula (d).

Now that we had the amount of mass we needed to find the solar masses so we divided the mass of the nebulae by one solar mass unity in the following equation. Our next part of this lab was to find the age of the nebulae m 57. We used the same formula and procedure as before to find the radius of the star. The distance from Earth was given to us to complete the small angel formula. We then needed to convert from the au to km by the following equation.

We were told the expansion of the nebulae to be 20 km / s and assumed this had been going on since the birth of the nebulae for simplicity of calculation. We figured this out in the following formula where is the distance and v is the velocity. After this we needed to convert from seconds to years so I went step by step (converting to minutes, hours, days, and years) and figured out the conversion factor to be 31, 536, 000 seconds in one year. This gave us the approx. age of the nebulae in years.

DATA The images used were loaded from the maxim program. The pixels were also found from manipulating the mouse over an area in the maxim program. Below are our following data.