Calculating with the previous equations gives an $E_{shot}$ of 5.1mJ, around that of GEDI (5mJ to 10mJ), but much higher than Icesat-2 (~100uJ).
Using the previous eye safety equations and the above $E_{shot}$ of 5.1mJ results in a $H_1$ of 6.49×10^-7 J/cm^2, which is slightly lower than the $MPE$ of 1.64×10^-6 J/cm^2. The fraction between the two is 0.395, implying that this LiDAR system is 2.5x below the eye safety limit. It can thus be assumed to be eye safe.
With the above $E_{shot}$ of 5.1mJ and the constraints of the Falcon-class satellite, we find a swath $s$ of 1.65m - which sounds very disappointing! But consider that this is an average swath that assumes the LiDAR is continuously firing using all available energy. We can take an approach instead similar to SAR, where we fire only for a short few seconds per orbit (say for 1 second out of every 2000 seconds). This will allow us to capture a greater than 3km swath, which is comparable to some Earth observation satellites (Black Sky and Satellogic). This would allow the satellite to focus on forested land, rather than pointlessly firing lasers into open ocean.
Such a satellite could capture 991sqkm per day, or 362,000sqkm per year. While this capacity pales in comparison to optical or SAR satellites, LiDAR has a much higher earning capacity. As previously mentioned, we can charge $1 per hectare ($100/sqkm) to comfortably outcompete aerial LiDAR, thereby resulting in an earning capacity of more than $36 million per satellite per year.
With a mission cost of $20 million, we see a 6.7 month payback period.
As fantastic as these satellites will be for earning revenue, how useful will they be for providing yearly updates for forests globally?
Using the method described previously, taking into account forest area, cloud cover, and the yearly coverage, we estimate that we will need a constellation of 461 satellites to measure the carbon in our forests every year. This sounds like a lot, given this would imply $9.2 billion in capex every 3 years. But given it unlocks an annual $70 billion market, this is fantastic.
But we can do better.
Revising our calculations for our Starship-class satellites, we find a significant boost from the increased receiver optics area and lower altitude. This results in a fantastic $E_{shot}$ = 0.6mJ.
Using the previous eye safety equations and the above $E_{shot}$ of 0.6mJ results in a $H_1$ of 7.64×10^-8 J/cm^2, which is slightly lower than the $MPE$ of 7.24×10^-7 J/cm^2. The fraction between the two is 0.105, implying that this LiDAR system is 9.5x below the eye safety limit. It can thus be assumed to be even more eye safe than the Falcon-class satellite LiDAR.
Given 10kW of payload orbit average power is available results in an average swath $s$ = 360m. This is more than 200x greater than the swath for the Falcon-class satellite, even though the Starship-class satellite is 8x the size.
This results in a coverage of 216,000sqkm per day or 78.8 million sqkm per year. This means, adjusting for cloud coverage, we only need a Starlink v3 form factor constellation of 2 satellites to cover the Earth’s forests every year!
And the economics of each satellite are ridiculous. Even assuming it costs the same per kg as our 2xPelicans - 2000kg vs 250kg - so $160 million in capex every 3 years per satellite, the earning potential of each satellite is almost $8 billion per year.
While the Falcon-class satellites needed almost 7 months to pay back their initial investment, these Starship-class satellites achieve a payback period of only 7 days.