To solve the question, we'll analyze the gravitational force formula that Lexy used:
[tex]\[
F_g = G \frac{(m_1)(m_2)}{r^2}
\][/tex]
where:
- [tex]\(F_g\)[/tex] is the force of gravity,
- [tex]\(G\)[/tex] is the gravitational constant,
- [tex]\(m_1\)[/tex] and [tex]\(m_2\)[/tex] are the masses involved,
- [tex]\(r\)[/tex] is the distance between the centers of the two masses.
In the given formula:
[tex]\[
F_g = G \frac{(3 \times 10^5 \, \text{kg})(6 \times 10^{24} \, \text{kg})}{[(6.4 \times 10^6 \, \text{m}) + (1.8 \times 10^5 \, \text{m})]^2}
\][/tex]
- [tex]\(3 \times 10^5 \, \text{kg}\)[/tex] is one of the masses ([tex]\(m_1\)[/tex]).
- [tex]\(6 \times 10^{24} \, \text{kg}\)[/tex] is the other mass ([tex]\(m_2\)[/tex]).
- The term [tex]\([(6.4 \times 10^6 \, \text{m}) + (1.8 \times 10^5 \, \text{m})]^2\)[/tex] represents the square of the distance between the centers of the two masses.
Given that [tex]\(6 \times 10^{24} \, \text{kg}\)[/tex] represents the mass of Earth (since the Earth's mass is approximately [tex]\(5.97 \times 10^{24}\, \text{kg}\)[/tex]), it's logical to deduce that [tex]\(3 \times 10^5 \, \text{kg}\)[/tex] must be the mass of the other object involved, which in this context is the space shuttle.
Therefore, [tex]\(3 \times 10^5 \, \text{kg}\)[/tex] represents the mass of the space shuttle.
Hence, the correct answer is:
the mass of the space shuttle
