Vraag 3

voorbeeld van een berekening:

Voor de oppervlakte van het cirkelvormige aanzicht van de planeet geldt:

A_{GJ1214b}=0{,}0150\cdot6{,}487\cdot10^{16}=9{,}731\cdot10^{14}\operatorname{m}^2A_{GJ1214b}=0{,}0150\cdot6{,}487\cdot10^{16}=9{,}731\cdot10^{14}\operatorname{mm}^2A_{GJ1214b}=0{,}0150\cdot6{,}487\cdot10^{16}=9{,}731\cdot10^{14}m^2A_{GJ1214b}=0{,}0150\cdot6{,}487\cdot10^{16}=9{,}731\cdot10^{14}^2A_{GJ1214b}=0{,}0150\cdot6{,}487\cdot10^{16}=9{,}731\cdot10^{14}~^2A_{GJ1214b}=0{,}0150\cdot6{,}487\cdot10^{16}=9{,}731\cdot10^{14}~m^2A_{GJ1214b}=0{,}0150\cdot6{,}487\cdot10^{16}=9{,}731\cdot10^{14}~mm^2A_{GJ1214b}=0{,}0150\cdot6{,}487\cdot10^{16}=9{,}731\cdot10^{14}~m^2A_{GJ1214b}=0{,}0150\cdot6{,}487\cdot10^{16}=9{,}731\cdot10^{14}~^2A_{GJ1214b}=0{,}0150\cdot6{,}487\cdot10^{16}=9{,}731\cdot10^{14}~m^2$A_{\mathrm{GJ} 1214 \mathrm{~b}}=0{,}0150 \cdot 6{,}487 \cdot 10^{16}=9{,}731 \cdot 10^{14} \mathrm{~m}^{2}.

Hieruit volgt voor de straal$rvan GJ1214b:

A_{GJ1214b}=\pi r^2\rightarrow r_{GJ1214b}=\sqrt{\frac{A_{GJ1214b}}{\pi}}=\sqrt{\frac{9{,}731 \cdot10^{14}}{\pi}}=1{,}760\cdot10^7\operatorname{m}A_{GJ1214b}=\pi r^2\rightarrow r_{GJ1214b}=\sqrt{\frac{A_{GJ1214b}}{\pi}}=\sqrt{\frac{9{,}731 \cdot10^{14}}{\pi}}=1{,}760\cdot10^7\operatorname{mm}A_{GJ1214b}=\pi r^2\rightarrow r_{GJ1214b}=\sqrt{\frac{A_{GJ1214b}}{\pi}}=\sqrt{\frac{9{,}731 \cdot10^{14}}{\pi}}=1{,}760\cdot10^7mA_{GJ1214b}=\pi r^2\rightarrow r_{GJ1214b}=\sqrt{\frac{A_{GJ1214b}}{\pi}}=\sqrt{\frac{9{,}731 \cdot10^{14}}{\pi}}=1{,}760\cdot10^7A_{GJ1214b}=\pi r^2\rightarrow r_{GJ1214b}=\sqrt{\frac{A_{GJ1214b}}{\pi}}=\sqrt{\frac{9{,}731 \cdot10^{14}}{\pi}}=1{,}760\cdot10^7mA_{GJ1214b}=\pi r^2\rightarrow r_{GJ1214b}=\sqrt{\frac{A_{GJ1214b}}{\pi}}=\sqrt{\frac{9{,}731 \cdot10^{14}}{\pi}}=1{,}760\cdot10^7~mA_{GJ1214b}=\pi r^2\rightarrow r_{GJ1214b}=\sqrt{\frac{A_{GJ1214b}}{\pi}}=\sqrt{\frac{9{,}731 \cdot10^{14}}{\pi}}=1{,}760\cdot10^7~mmA_{GJ1214b}=\pi r^2\rightarrow r_{GJ1214b}=\sqrt{\frac{A_{GJ1214b}}{\pi}}=\sqrt{\frac{9{,}731 \cdot10^{14}}{\pi}}=1{,}760\cdot10^7~mA_{GJ1214b}=\pi r^2\rightarrow r_{GJ1214b}=\sqrt{\frac{A_{GJ1214b}}{\pi}}=\sqrt{\frac{9{,}731 \cdot10^{14}}{\pi}}=1{,}760\cdot10^7~A_{GJ1214b}=\pi r^2\rightarrow r_{GJ1214b}=\sqrt{\frac{A_{GJ1214b}}{\pi}}=\sqrt{\frac{9{,}731 \cdot10^{14}}{\pi}}=1{,}760\cdot10^7~mA_{GJ1214~b}=\pi r^2\rightarrow r_{GJ1214b}=\sqrt{\frac{A_{GJ1214b}}{\pi}}=\sqrt{\frac{9{,}731 \cdot10^{14}}{\pi}}=1{,}760\cdot10^7~mA_{GJ1214~b}=\pi r^2\rightarrow r_{GJ1214~b}=\sqrt{\frac{A_{GJ1214b}}{\pi}}=\sqrt{\frac{9{,}731 \cdot10^{14}}{\pi}}=1{,}760\cdot10^7~m$A_{\mathrm{GJ} 1214 \mathrm{~b}}=\pi r^{2} \rightarrow r_{\mathrm{GJ} 1214 \mathrm{~b}}=\sqrt{\frac{A_{\mathrm{GJ} 1214 \mathrm{~b}}}{\pi}}=\sqrt{\frac{9{,}731 \cdot 10^{14}}{\pi}}=1{,}760 \cdot 10^{7} \mathrm{~m}.

Hieruit volgt\frac{r_{GJ1214b}}{r_{\text{aarde }}}=\frac{1{,}760 \cdot10^{7}}{6{,}371 \cdot10^{6}}=2{,}76$\frac{r_{\mathrm{GJ} 1214 \mathrm{~b}}}{r_{\text {aarde }}}=\frac{1{,}760 \cdot 10^{7}}{6{,}371 \cdot 10^{6}}=2{,}76.