Radar Ranging of Venus for AST 1040

Statement of Purpose:  Determine the distance and diameter of Venus based on radar data and arc seconds recorded on 3 separate dates.

Statement of Procedure:  The data given was in minutes and seconds.  The first step in this procedure was to convert those times into seconds by multiplying the minutes by 60 and adding the remaining seconds.  These were the times of a round-trip to Venus and back on radar beams (which travel at the speed of light).   The time it takes light to travel to and back from Venus can tell us the distance to Venus.  Light travels at 300,000km/s and our first trip took 574s.  So we can find the distance by multiplying our recorded time by the speed of light and dividing by two (for half the round-trip): (574x300000)/2 = 86100000km.  Then using the graphic we can count the apparent arc seconds of Venus at the same time the radar beams were sent.  The arc seconds are then converted into degrees by dividing by 3600 (since there are 3600 arc seconds in a degree).   Using this Angular Size and the Distance, we can find the true size of Venus by multiplying the two and dividing the sum by 57.3 degrees (Radian).  Using the data of 3 dates, we can average our measurements by adding all three and dividing by three.

Data:

Date	One-way Timing (sec)	True Distance (km)	# of ticks	Angular Size in degrees	True Diameter(km)
11/15/2005	574	8.61 x 107	29	0.0080555556	12104
11/30/2005	426	6.39 x 107	36	0.01	11152
12/15/2005	364	5.46 x 107	47	0.0130555556	12440
Average					11899

Statement of Conclusion:  The actual diameter of Venus is 12103.6km.  So my results weren’t too far off (204.6km difference).  Considering I was using data recorded by someone other than myself, I’m not exactly sure what I could have done differently to get a more accurate result.  I did consider rounding the angular size but noticed quickly that my results became further off after rounding.

1)      Could this procedure be used with other astronomical bodies such as the Sun, Mars or Jupiter?  Why or Why not? 

a.       Depending on the body’s composition will determine whether or not this method may or may not work.   If an object has an atmosphere, radar (radio) waves may or may not be able to penetrate the atmosphere depending on its composition and density.   This procedure can only be used if the wavelength of the sent beam will penetrate and return through the atmosphere of the object (if it has one).  This method will almost always work with objects in our solar system which do not have an atmosphere and have a measurable angular size.

2)      Why would this method not be used with distant stars?  (There may be more than one answer here.)

a.       The closest star (Proxima Centauri) is 4.2 light years away.  That means a round trip at the speed of light from Earth to Proxima Centauri would take 8.4 years.  Considering the Earth’s rotation and orbit, this procedure would take precise timing and calculations to send a signal and receive the bounced signal 8.4 years later.  And then only if Proxima Centauri (or another object) has a penetrable atmosphere.

b.      The other problem with this method is getting an accurate reading on the angular size of a distant star.  Even Proxima Centauri is so far away that getting an accurate reading on its angular size would be incredibly difficult if not improbable.

c.       Another problem would be that the signal would gradually lose intensity as it travels further.  The returning echo (if there is a return echo) would be so faint, it would be nearly impossible to detect.

d.      Another problem might be finding an unobstructed direct path to a distant star.  The space between may be filled with particles, gasses, ice, or other objects that may absorb, deflect, scatter or even bend our sent light signal.

3)      What would be different if we used data for different dates?

a.       If the dates were different in this exercise the distance of, and therefore the angular size of Venus would be different.   As both Earth and Venus travel around the Sun in their respective orbits, Venus may appear to have a larger or smaller angular size depending on its respective distance to Earth.  While the angular size might change, the radar beams should also change, respectively.  If Venus is closer to Earth, Venus will have a larger angular size and a shorter radar time.  If Venus is farther from Earth, it will have a smaller angular size and a longer radar time.  The radar time and angular size of Venus will change in proportion to each other.

4)    Would this procedure work with other forms of electromagnetic radiation such as visible light or infrared light?  Why or why not?

a.       This procedure will work with other forms of electromagnetic radiation given the object being measured.  The moon is currently under scrutinous observation with laser beams (visible light).  However, depending on the atmosphere of the object being measured will determine whether this method will or will not work (see question 1).   The wavelength of the light must be able to reflect off of the object’s surface and return to Earth.  Unless, of course, the object’s atmosphere is what is being studied.  If the object has no atmosphere, this method would probably work with most forms of light.