Question

10 formula 1 point a 702.771 kg space ship is in orbit around an asteroid. the distance between the center of the space ship and the center of the asteroid is 446 meters. the space ship experiences a gravitational force equal to 0.02 newtons form the asteroid. determine the mass of the asteroid in kg. report your answer in standard floating notation. answer

Explanation:

Step1: Write the formula for gravitational force

The formula for gravitational force is \( F = G\frac{m_1m_2}{r^2} \), where \( F \) is the gravitational force, \( G = 6.67\times10^{- 11}\space Nm^{2}/kg^{2} \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two objects, and \( r \) is the distance between their centers.
We need to solve for \( m_2 \) (mass of the asteroid). Rearranging the formula gives \( m_2=\frac{F\times r^{2}}{G\times m_1} \).

Step2: Substitute the given values

Given \( F = 0.02\space N \), \( r = 446\space m \), \( m_1=702.771\space kg \), and \( G = 6.67\times 10^{-11}\space Nm^{2}/kg^{2} \).
Substitute into the formula:

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First, calculate the denominator \( 6.67\times 10^{-11}\times702.771\approx4.697\times10^{-8} \).
Then \( m_2=\frac{3978.32}{4.697\times 10^{-8}}\)

$$ m_2=\frac{3978.32}{4.697}\times10^{8}\approx847.0\times10^{8}=8.47\times 10^{10}\space kg$$

Answer:

\(8.47\times 10^{10}\)