If $F = \frac{G M m}{d^{2}}$ $F=(GMm)/d^2$ , then $d =$ $d=$ ?

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Answer 1 · 2016-06-09T22:16:22

$d = \sqrt{\frac{G M m}{F}}$ $d=sqrt((GMm)/F)$

Given,

$F = \frac{G M m}{d^{2}}$ $F=(GMm)/d^2$

Multiply both sides by $d^{2}$ $d^2$ .

$F \cdot d^{2} = \frac{G M m}{d^{2}} \cdot d^{2}$ $Fcolor(red)(*d^2)=(GMm)/d^2color(red)(*d^2)$

Simplifying,

$F*d^2=(GMm)/color(red)cancelcolor(black)(d^2)*color(red)cancelcolor(black)(d^2)$

$F*d^2=GMm$

Divide both sides by $F$ .

$color(red)((color(black)(F*d^2))/F)=color(red)((color(black)(GMm))/F)$

Simplifying,

$(color(red)cancelcolor(black)F*d^2)/color(red)cancelcolor(black)F=(GMm)/F$

$d^2=(GMm)/F$

Take the square root of both sides.

$color(red)(sqrt(color(black)(d^2)))=color(red)(sqrt(color(black)((GMm)/F)))$

Simplifying,

$d=color(green)(|bar(ul(color(white)(a/a)color(black)(sqrt((GMm)/F))color(white)(a/a)|)))$

If F=(GMm)/d^2F=GMmd2F=(GMm)/d^2, then d=d=d=?