Vraag 25

uitkomst:$g_{\mathrm{b}}=0{,}90 g_{\text {aarde }}

voorbeeld van een berekening:

methode 1

Voor de valversnelling$ggeldt:$F_{\mathrm{z}}=F_{\mathrm{g}}. Hieruit volgt:

$m g=G \frac{m M}{r^{2}} \rightarrow g_{\mathrm{b}}=G \frac{M_{\mathrm{b}}}{r_{\mathrm{b}}^{2}}=6{,}674 \cdot 10^{-11} \frac{1{,}3 \cdot 5{,}972 \cdot 10^{24}}{(1{,}2 \cdot 6{,}371 \cdot 10^{6})^{2}}=8{,}86 \mathrm{~ms}^{-2}.

Dus:$g_{\mathrm{b}}=(\frac{8{,}86}{9{,}81}) g_{\text {aarde }}=0{,}90 g_{\text {aarde }}.

of

methode 2

Voor de valversnelling g geldt:F_{z}=F_{g}F_{z}=FF_{z}=F_{z}F. Hieruit volgt:

mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=0{,}90g_{aarde}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=0{,}90g_{aard}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=0{,}90g_{aar}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=0{,}90g_{aa}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=0{,}90g_{a}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=0{,}90g_{a}dmg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=0{,}90g_{a}demg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=0{,}90g_{a}dmg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=0{,}90g_{a}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=0{,}90g_{a}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=0{,}90g_{a}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=0{,}90gmg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=0{,}90mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=0{,}9mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=0{,}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=0mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}=mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}^2}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^{}}}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde^2}}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aarde}}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aard}}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aar}}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{aa}}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r_{a}}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{r}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot\frac{GM_{aarde}}{\placeholder{}}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot GM_{aarde}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot GM_{aard}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot GM_{aar}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot GM_{aa}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot GM_{a}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot GMmg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdot Gmg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}\cdotmg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}44}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}4}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1{,}}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{1}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=\frac{1{,}3}{\placeholder{}}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=1{,}3mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=1{,}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=1mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}=mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)^2}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aarde}\right)}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aard}\right)}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aar}\right)}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{aa}\right)}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r_{a}\right)}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot r\right)}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\cdot\right)}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}2\right)}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1{,}\right)}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(1\right)}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\left(\placeholder{}\right)}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=\frac{G\cdot1{,}3\cdot M_{aarde}}{\placeholder{}}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=G\cdot1{,}3\cdot M_{aarde}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=G\cdot1{,}3\cdot M_{aard}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=G\cdot1{,}3\cdot M_{aar}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=G\cdot1{,}3\cdot M_{aa}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=G\cdot1{,}3\cdot M_{a}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=G\cdot1{,}3\cdot Mmg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=G\cdot1{,}3\cdotmg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=G\cdot1{,}3mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=G\cdot1{,}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=G\cdot1mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=G\cdotmg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=Gmg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}=mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r_{b}^2}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r^2}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{r}mg=G\frac{mM}{r^2}\rightarrow g_{b}=\frac{GM_{b}}{\placeholder{}}mg=G\frac{mM}{r^2}\rightarrow g_{b}=GM_{b}mg=G\frac{mM}{r^2}\rightarrow g_{b}=GMmg=G\frac{mM}{r^2}\rightarrow g_{b}=Gmg=G\frac{mM}{r^2}\rightarrow g_{b}=mg=G\frac{mM}{r^2}\rightarrow g_{b}mg=G\frac{mM}{r^2}\rightarrow gmg=G\frac{mM}{r^2}\rightarrow g-mg=G\frac{mM}{r^2}\rightarrow g-mg=G\frac{mM}{r^2}\rightarrow gmg=G\frac{mM}{r^2}\rightarrowmg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r^2}mg=G\frac{mM}{r}mg=G\frac{mM}{\placeholder{}}mg=GmMmg=Gmmg=Gmg=mgm