Question

problem 2
space debris is becoming a problem surrounding the earth. the force between
two equal masses of space debris is given by ( 2 \times 10^{-12} n ). the distance
between the two objects is found to be ( r = 10 km ). find the mass of each of
these space objects ( (m =?) ).

Explanation:

Step1: Convert the distance unit

Convert \(r = 10\space km\) to \(m\). Since \(1\space km=1000\space m\), then \(r = 10\times1000=10^{4}\space m\).

Step2: Use the gravitational force formula

The gravitational force formula is \(F = G\frac{M_1M_2}{r^{2}}\). Here \(M_1 = M_2 = M\), \(F=2\times 10^{-12}\space N\), and \(G = 6.67\times 10^{-11}\space N\cdot m^{2}/kg^{2}\).
Substitute into the formula: \(2\times 10^{-12}=6.67\times 10^{-11}\times\frac{M\times M}{(10^{4})^{2}}\).

Step3: Solve for \(M\)

First, simplify the equation:

$$
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$$

Answer:

The mass of each space object is approximately \(1732\space kg\).