1. 1 TRANSIT. Sat05_72.ppt, 2005-12-05. Doppler-effect used: In the orbit Distant observer

2. 2 TRANSIT. Sat05_72.ppt, 2005-12-05. Doppler effect: f s = from satellite f r =received v=velocity

3. 3 TRANSIT. Sat05_72.ppt, 2005-12-05..

4. 4 Doppler-count. Sat05_72.ppt, 2005-12-05.. We count integer number of changes, N.

5. 5 Integrated Doppler count. Sat05_72.ppt, 2005-12-05. r ij r jk

6. 6 Observation equations. Sat05_72.ppt, 2005-12-05.

7. 7 TRANSIT. Sat05_72.ppt, 2005-12-05. f: 400 MHz=4x10 8 Hz and 150 MHz λ= 0.75 m 2 m Velocity 7.5 km/s In 1 s 7.5 km shorter in line of sight: 1.875x10 -5 shorter Wavelength: λ 1 = λ+Δλ=0.75001875 m=c/f 1 f 1 =400.01 MHz, Δf=10 kHz

8. 8 Example. Sat05_72.ppt, 2005-12-05. Equator: Velocity at surface of the Earth: 6371 km x 0.000073 s -1 =0.465 km/s Δf=400 MHz * 0.465/300000 = 0.62 kHz Exercise: We are at the North-Pole. Satellite with i=90 0, e=0, R e =6371 km, v=7.5 km/s. What is a ? What is the Doppler-shift when the satellite rizes above the horizon ? What is the corresponding change of distance per minute ?

9. 9 Principles. Sat05_72.ppt, 2005-12-05. Doppler method basic ideas bedind GPS. Used: Polar orbits, h=1100 km Observation time 15 – 20 m. 2 frequencies to eliminate Ionosphere influence from quarz-ocillator 5 Mhz multiplied with 30 or 80. Time signal every 2. minute Broadcasts Kepler elements Error in static positioning: 1 m after 10 days of observation (Greenland only 3 days !)

10. 10 Accuracy. Sat05_72.ppt, 2005-12-05.