As part of our ongoing work to provide an Earth-Venus-Earth (EVE) communications link budget, we have updated several sections of the Jupyter Lab notebook.
Link Budget Document Locations
A PDF version of the EVE link budget (lots of updates) is here: https://github.com/OpenResearchInstitute/documents/blob/master/Engineering/Link_Budget/Link_Budget_Modeling.pdf
The Jupyter Lab notebook is available right here: https://github.com/OpenResearchInstitute/documents/blob/master/Engineering/Link_Budget/Link_Budget_Modeling.ipynb
Explaining Doppler Spread
Doppler spread happens when our signal reflects off a rotating structure, like Venus. Part of Venus (the East limb, on the right side of Venus as viewed from Earth) is moving towards us. And, part of Venus is moving away from us (the West limb, on the left side of Venus as viewed from Earth). The parts moving towards us cause reflected frequencies to increase. In the radar community, when a target is moving towards you, it produces a negative Doppler shift. The parts moving away from us cause reflected frequencies to decrease. In the radar community, when a target is moving away you, it produces a positive Doppler shift. The signal reflected off the center of the planet is reflected back with little to no frequency change. Doppler spread is a quantification of how muddled up our reflected signal becomes due to the rotation of the reflector.
Gary K6MG writes “A rough calculation of venus limb-to-limb doppler spreading @ 1296MHz: 4 * venus rotation velocity 1.8 m/s / 3e8 m/s * 1.296e9 c/s = 31 c/s. This calculation is the same as K1JT uses for EME in Frequency-Dependent Characteristics of the EME Path and is motivated from first principles. One edge of Venus is approaching the earth at a 1.8m/s velocity relative to the center of Venus, the other edge is receding at the same velocity giving one factor of 2. The other factor of 2 is due to the reflection, the wave is shortened or lengthened on both the approach and the retreat.”
You may be curious as to how the wave can be shortened or lengthened on both the approach and the retreat.
The double Doppler shift happens because radar involves a two-way journey of the radio wave. For example, a station on Earth may transmit a radio wave at exactly 1296 MHz. This wave travels toward Venus. When the wave hits a moving point on Venus’s surface (like the East or West limb), the wave’s frequency as experienced by that point is different from what was transmitted.
If the point is moving away from Earth, it “sees” a lower frequency (in other words, a redshift). If the point is moving toward Earth, it “sees” a higher frequency (in other words, a blueshift). The wave bounces off part of Venus’s surface. The wave is now re-emitted at the shifted frequency that the moving point “sees” or experiences. So the reflected wave already has one Doppler shift applied. As this already-shifted wave travels back to Earth, a second Doppler shift occurs. This is because the reflecting point is still moving, so the wave gets compressed or stretched again. The wave returns to Earth with two Doppler shifts applied. Therefore, there is a factor of two in the equation explained by Gary K6MG.
An example with real-world objects can help visualize what’s going on. Imagine throwing a tennis ball at a person on a moving train, and the train is coming right at you. You throw the ball to the person on the train at 10 mph. To the person on the train, your 10 mph ball appears to be moving faster or slower depending on the train’s direction. Since they are moving towards you, your 10 mph ball’s speed is added to the train’s 30 mph speed, and the ball would arrive at what felt like 40 mph. From their perspective, they received a 40 mph ball. Now they are just going to “reflect” the ball back at you at the same relative force as they received it. Now the ball is coming back to you at that 40 mph plus the velocity of the train, which is 30 mph. So you are going to be catching a 70 mph fast ball! When you receive the ball, its speed has been affected twice by the train’s motion.
This works in the other direction as well. Now that the train is moving away from you, it’s a lot harder to catch up to. So, you get a baseball pro, your friend Shohei Ohtani, to throw the ball for you. The train is moving away from you at 30 mph. Ohtani throws the ball at 100 mph. The person on the train catches it. It arrives at what feels like 70 mph to the person on the train. He tosses it back to Ohtani at 70 mph, because that’s how fast it arrived, relative to him. The train takes another 30 mph off the velocity of the ball, and Ohtani catches a ball going 40 mph.
The important insight about radar returns off of moving objects is that the reflection does not simply “bounce back” the original frequency. The moving reflector actually re-emits the signal at the Doppler-shifted frequency it receives, and then this already-shifted frequency undergoes a second Doppler shift on its return journey.
Doppler Shift Challenge
While driving your car, you are stopped for running a red light. You tell the police officer that because of the Doppler shift, the red light (650 nm) was blueshifted to a green light (470 nm) as you drove towards the stop light. How fast would you have to be going in order for this to be true?
A) 0.5 times the speed of light
B) 0.3 times the speed of light
C) 0.1 times the speed of light
D) 0.01 times the speed of light
E) 70 mph