BHEX Mini
Direct Imaging Black Holes from LEO
Ref Bari | Update to Ben 07/22
BHEX Mini SWaPC
Size
Weight
Power
Power
Cost
\sim 2.5m
\sim 25-50kg
22 kg
300W
400mW @15^{\circ}K
\$10 \text{mln}
754 mm \times \\ 146 mm \times \\ 300 mm
\$2-5 \text{Mln}
\$4-11 \text{Mln}
10-20W
\text{(deployment)}
5-7 kg
\sim 10W
\sim \$ 1 \text{mln}
\sim0.02m^3
\sim 1 kg
\sim 3W
\sim \$1\text{mln}^*
60 mm\times \\60mm \times \\32 mm
1U (100 mm\times \\100 mm \times \\100 mm)
1.2 kg
1.2 kg
100W\\\text{generated}
\sim \$100\text{k}
3U (300 mm\times \\300 mm \times \\300 mm)
100W
3 kg
\sim \$1\text{mln}^*
\sim 4W
\sim 1 kg^*
12 mm \times \\12 mm
\sim \$1\text{mln}^*
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
Systems Design
SEFD
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 67,000 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 100K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\text{SEFD}_{\text{BHEX}}\sim 18,000 \text{ Jy}
\text{SEFD}_{\text{ALMA}}\sim 74 \text{ Jy}
\text{SEFD}_{\text{SMA}}\sim 6700 \text{ Jy}
\text{SEFD}_{\text{SMT}}\sim 10,500 \text{ Jy}
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}=\frac{1}{\eta_{\mathrm{Q}}} \sqrt{\frac{\mathrm{SEFD}_{\mathrm{BHEX}} \mathrm{SEFD}_{\text{BHEX-Mini}}}{2 \Delta \nu \Delta t}}
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}=\frac{1}{\eta_{\mathrm{Q}}} \sqrt{\frac{\mathrm{SEFD}_{\mathrm{BHEX}} \mathrm{SEFD}_{\text{BHEX-Mini}}}{2 \Delta \nu \Delta t}}
\sigma_{\text{BHEX Mini - EHT}}=\frac{1}{\eta_{\mathrm{Q}}} \sqrt{\frac{\mathrm{SEFD}_{\mathrm{EHT}} \mathrm{SEFD}_{\text{BHEX-Mini}}}{2 \Delta \nu \Delta t}}
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}=\frac{1}{0.75} \sqrt{\frac{(18,000 \text{ Jy})(20,080 \text{Jy})}{2 (32 \text{GHz}) (100s)}}
\sigma_{\text{BHEX Mini - EHT}}=\frac{1}{0.75} \sqrt{\frac{(6000 \text{ Jy})(20,080 \text{Jy})}{2 (32 \text{GHz}) (10s)}}
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 2\pi \cdot f \cdot \sigma_t
\sigma_t = \sigma_f \cdot \Delta t
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 2\pi \cdot f \cdot \sigma_t
\sigma_t = \sigma_f \cdot \Delta t
\sigma_t = 8\cdot 10^{-15} (\text{LISA USO})
\Delta \phi = 2\pi \cdot (86\cdot 10^9 \text{ Hz}) \cdot 8\cdot 10^{-15}s\sim 10^{-3} \text{ rad}<1 \text{ rad}
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\Delta t = \text{10 s})
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\Delta t = \text{10 s})
L = 1-\exp\left(-2\pi^{2}f^{2}t^{2}\sigma_y^{2}\right)
L = 1-\exp\left[-2\pi^{2}(86\cdot 10^9)^{2}(10)^{2}(5\cdot 10^{-11})^{2}\right]\sim 1\%
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})
L\sim 1\% \text{ (JUICE USO)}
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})
L\sim 1\% \text{ (JUICE USO)}
\operatorname{Rate}(\mathrm{bps})=N_{\text {bits }} \times \Delta \nu \times 2_{\text {pol }} \times 2_{\text {Nyquist }}
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})
L\sim 1\% \text{ (JUICE USO)}
\operatorname{Rate}(\mathrm{bps})=N_{\text {bits }} \times \Delta \nu \times 2_{\text {pol }} \times 2_{\text {Nyquist }}
\text{Rate}\times T_{orb} \times \text{Duty Cycle} = \text{Total Data (GB)}
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})
L\sim 1\% \text{ (JUICE USO)}
\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}
\theta_{S-S} \sim \frac{\lambda}{D}
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})
L\sim 1\% \text{ (JUICE USO)}
\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}
\theta_{S-S} \sim \frac{\lambda}{D}=\frac{3.5mm}{20,000 km}
\theta_{S-G} \sim \frac{\lambda}{D}=\frac{3.5mm}{400 km}
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})
L\sim 1\% \text{ (JUICE USO)}
\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}
\theta_{\text{BHEX Mini -BHEX}}\sim 35 \mu as
\theta_{\text{BHEX Mini - EHT}} \sim 1800 \mu as
Systems Design
\sim85.3 kg
\sim 437 W
\sim \$25\text{ million}
N/A
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})
L\sim 1\% \text{ (JUICE USO)}
\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}
\theta_{\text{BHEX Mini -BHEX}}\sim 35 \mu as
\theta_{\text{BHEX Mini - EHT}} \sim 1800 \mu as
\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}
Systems Design
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})
L\sim 1\% \text{ (JUICE USO)}
\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}
\theta_{\text{BHEX Mini -BHEX}}\sim 35 \mu as
\theta_{\text{BHEX Mini - EHT}} \sim 1800 \mu as
\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}
\tau<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}
Systems Design
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})
L\sim 1\% \text{ (JUICE USO)}
\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}
\theta_{\text{BHEX Mini -BHEX}}\sim 35 \mu as
\theta_{\text{BHEX Mini - EHT}} \sim 1800 \mu as
\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}
\tau<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}
\omega=\frac{2\pi}{P} = \frac{2\pi}{1.5 \text{ hr}\cdot \frac{3600 s}{1 \text{hr}}}=1.16\times 10^{-3} rad/s
Systems Design
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})
L\sim 1\% \text{ (JUICE USO)}
\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}
\theta_{\text{BHEX Mini -BHEX}}\sim 35 \mu as
\theta_{\text{BHEX Mini - EHT}} \sim 1800 \mu as
\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}
\tau<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}
0.11 G \lambda < b_{s g}<3.5 G \lambda
Systems Design
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})
L\sim 1\% \text{ (JUICE USO)}
\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}
\theta_{\text{BHEX Mini -BHEX}}\sim 35 \mu as
\theta_{\text{BHEX Mini - EHT}} \sim 1800 \mu as
\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}
\tau<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}
\theta_{FOV} = 180 \mu as
Systems Design
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})
L\sim 1\% \text{ (JUICE USO)}
\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}
\theta_{\text{BHEX Mini -BHEX}}\sim 35 \mu as
\theta_{\text{BHEX Mini - EHT}} \sim 1800 \mu as
\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}
\tau<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}=\frac{1}{(1.16\times 10^{-3} \frac{rad}{s}) (3.5 G\lambda)(1.6\cdot 10^{-7}s)}
Systems Design
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})
L\sim 1\% \text{ (JUICE USO)}
\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}
\theta_{\text{BHEX Mini -BHEX}}\sim 35 \mu as
\theta_{\text{BHEX Mini - EHT}} \sim 1800 \mu as
\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}
\tau_{\text{BHEX-Mini}}\lessapprox \frac{15G\lambda}{3.5 G\lambda}\lessapprox 4.2 \text{ min}, \tau_{\text{Coherence, BHEX-Mini}}\lessapprox 2 \text{ min} \sim 120 s
Systems Design
\text{SEFD}_{\text{BHEX-Mini}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 20,080 \text{ Jy}
T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K
T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K
T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy
SEFD
USO
Data
\theta_{\text{Res}}
Orbit
\sigma_{\text{Noise}}
\tau_{\text{max}}
\sigma_{\text{BHEX Mini - BHEX}}\sim 10 \text{ mJy}
\sigma_{\text{BHEX Mini - EHT}}\sim 18 \text{ mJy}
\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})
L\sim 1\% \text{ (JUICE USO)}
\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}
\theta_{\text{BHEX Mini -BHEX}}\sim 35 \mu as
\theta_{\text{BHEX Mini - EHT}} \sim 1800 \mu as
\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}
\tau_{\text{Coherence, BHEX-Mini}}\lessapprox 2 \text{ min} \sim 120 s
Time-Resolving Sgr A*
Time-Resolving Sgr A*
\tau<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}
\text{Coherence Time}
Time-Resolving Sgr A*
\tau<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}
\text{Coherence Time}
\omega:\text{Angular Velocity of Satellite}
\omega=\frac{2\pi}{P} = \frac{2\pi}{1.5 \text{ hr}\cdot \frac{3600 s}{1 \text{hr}}}=1.16\times 10^{-3} rad/s
Time-Resolving Sgr A*
\tau_{max}<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}
\text{Coherence Time}
D_\lambda:\text{Longest Baseline in } \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda
Time-Resolving Sgr A*
\tau<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}
\text{Coherence Time}
\theta_{FOV}:\text{Angular Extent of Radio Target}
\theta_{FOV} = 180 \mu as
Time-Resolving Sgr A*
\tau<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}=\frac{1}{(1.16\times 10^{-3} \frac{rad}{s}) (3.5 G\lambda)(1.6\cdot 10^{-7}s)}
\text{Coherence Time}
\tau_{\text{BHEX-Mini}}\lessapprox \frac{15G\lambda}{3.5 G\lambda}\lessapprox 4.2 \text{ min}
\tau_{\text{Coherence, BHEX-Mini}}\lessapprox 2 \text{ min} \sim 120 s
Time-Resolving Sgr A*
\sigma=\frac{1}{\eta_{\mathrm{Q}}} \sqrt{\frac{\mathrm{SEFD}_1 \mathrm{SEFD}_2}{2\cdot \Delta \nu \cdot \tau}}
\text{Thermal Noise on Baselines}
Time-Resolving Sgr A*
\sigma=\frac{1}{\eta_{\mathrm{Q}}} \sqrt{\frac{\mathrm{SEFD}_1 \mathrm{SEFD}_2}{2\cdot \Delta \nu \cdot \tau}}
\text{Thermal Noise on Baselines}
\eta_{Q}(N_{bit})\sim 1-\frac{\pi}{2}\cdot 2^{-2N_{bit}}
Quantization Efficiency: how much of the analog SNR is retained after digitization
\eta_{Q}(1)\sim 63\%
\eta_{Q}(2)\sim 88\%
Time-Resolving Sgr A*
\sigma=\frac{1}{\eta_{\mathrm{Q}}} \sqrt{\frac{\mathrm{SEFD}_1 \mathrm{SEFD}_2}{2\cdot \Delta \nu \cdot \tau}}
\text{Thermal Noise on Baselines}
SEFD_{ALMA} \sim 150 Jy
SEFD_{BHEX} \sim 20,000Jy
SEFD_{Ground Telescope} \sim 10,000Jy
BHEX Mini
Sub-milli arcsecond angular resolution:
Dual short and long baseline lengths
Rapid coverage of (u,v) plane
Decreased signal loss from LEO
Decreased radiation environment in LEO vs. MEO
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as
5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda
T_{orb}=90 \text{ min}
- What is the integration time for BHEX Mini on the (u,v) plane?
- Could BHEX Mini possibly enable direct imaging of dynamic accretion disk around Sgr A*? (i.e., creating a movie of a black hole!)
BHEX Mini
\text{To time resolve Sgr A*, we must have} \\f_{coverage}>50\% \text{ in } t < T_{ISCO} \sim 30 \text{ min}
BHEX Mini
\tau<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}
\sigma=\frac{1}{\eta_{\mathrm{Q}}} \sqrt{\frac{\mathrm{SEFD}_1 \mathrm{SEFD}_2}{2 \Delta \nu \tau}}
\text{Coherence Time}
\text{Thermal Noise}