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A probe orbiting venus exerts a gravitational force of 2. 58 Γ— 103 n on venus. Venus has a mass of 4. 87 Γ— 1024 kg. The mass of the probe is 655 kilograms. The gravitational constant is 6. 67 Γ— 10-11 n*m2/kg2. To three significant digits, the probe is Γ— 106 m from the center of venus.

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Answer:

[tex]\mathrm{9.08 \times 10^6 \:km}[/tex]

Explanation:

To solve for the distance between the probe and Β the center of Venus, use the formula:

[tex]\mathrm{F = \frac{G\: m1 \:m2}{r^2}}[/tex]

Β 

Plugin the values:

G =

[tex]6.67\times10^{-11} \mathrm{\frac{m3}{kg\: s2}}[/tex]

[tex]\mathrm{F} =2.58 \times 10^3\mathrm{N}[/tex]

[tex]\mathrm{m1 = 4.87 \times 10^{24}\:kg}[/tex]

[tex]\mathrm{m2 = 655\: kg}[/tex]

Hence:

[tex]\mathrm{F = \frac{G\: m1 \:m2}{r^2}}[/tex]

[tex]2.58 \times 10^{23} = 6.67 \times 10^{-11} (4.87 \times 10^{24})[/tex]

[tex]\frac{(655)}{r^2}[/tex]

[tex]\mathrm{r = 9.08 \times 10^6 \:km}[/tex]

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