Question

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

Answer 1

Answer:

$\mathrm{9.08 \times 10^6 \:km}$

Explanation:

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

$\mathrm{F = \frac{G\: m1 \:m2}{r^2}}$

 

Plugin the values:

G =

$6.67\times10^{-11} \mathrm{\frac{m3}{kg\: s2}}$

$\mathrm{F} =2.58 \times 10^3\mathrm{N}$

$\mathrm{m1 = 4.87 \times 10^{24}\:kg}$

$\mathrm{m2 = 655\: kg}$

Hence:

$\mathrm{F = \frac{G\: m1 \:m2}{r^2}}$

$2.58 \times 10^{23} = 6.67 \times 10^{-11} (4.87 \times 10^{24})$

$\frac{(655)}{r^2}$

$\mathrm{r = 9.08 \times 10^6 \:km}$