Distances to the Planets |
In order to measure the diameter of a planet, we
must first know its distance. Since about the mid-19th Century,
astronomers have had a reasonably good idea of the distance to
the Sun, and hence through Kepler's Third Law a good idea of the
distances to the planets.
Mars image from the Hubble Space Telescope, courtesy of NASA
However, today we have a much more precise method of measuring distances to the planets -- radar. Radar is just a form of radio transmission (RADAR = " RA dio D etection A nd R anging"). Radio waves travel at a precise speed through a vacuum: 299,792,458 meters per second, which usually is rounded to 300,000 km/s.
If, for example, a radar beam is directed at the Moon and the return signal is received 2.58 seconds later, then the distance is 1.29 seconds times the 300,000 km/s, which equals 387,000 km. We take half the time interval because the full interval is for the round trip to the Moon and back. (By the way, modern radar equipment can be considerably more accurate than to the hundredths of a second, but that is plenty of accuracy for this example.)
Now try your hand at this activity. On May 1, 1999, astronomers at the Jet Propulsion Lab in Pasadena directed that a radio telescope in Owens Valley send a radio beam to Mars to gauge the current distance. At the same time, astronomers at the large Hale telescope on Mount Palomar measured the angular diameter of Mars. The radio signal was transmitted and the reflected signal returned 48 minutes, 6.54 seconds later. Simultaneously, the optical astronomers at Hale measured the angular size of Mars as 16.18 seconds of arc.
So, now your activity is to calculate the distance to Mars, and from that plus the Angular Diameter AD, find the true size of Mars. To find the true diameter, TD, use this equation:
TD=AD*Distance/57.3
When you are ready, you can check your answers here: ANSWER
(Note: this example is made up, but the data is real. If you prefer, you can do this activity with a planet or the Moon in the real sky. You need to measure the angular diameter. Since you most likely don't have access to a radio telescope for the distance measurement, you can get that from your planetarium software or from many online services. Just remember to get the instantaneous distance from Earth at the time of your measurement, NOT the average distance. Measuring angular size is relatively easy to do with a telescope, but small angles require a large telescope. You could easily estimate the angular size of the Moon just by timing how long it takes to pass a certain point due to the Earth rotation, which is 15 degrees per hour).
(Use Your Planetarium Software)
1) Open your Planetarium software.
2) Across the top you should see the options:
File - Edit - Set - Field - Center - Animation - Miscellaneous -
Help .
From this bar click on "Field," then "Chart Mode"
and finally "Local Horizon."
3) Under "Set," click on "Time" and then "Enter Local Time." Set the time for about 18:00 hours on May 1, 1999. (You can use other dates, of course, but be aware that you will get different values for distance since Mars is always moving relative to Earth.)
4) Under "Center," select "On solar system object" and then Mars.
5) Mars should now be centered in your view. Click on it to get the information box, and use the data there to complete the activity as outlined above.
Back