Kepler's Third Law Essay

Calculation: Use Kepler’s Third Law (M=(4π^2 r^3)/(GP^2 )) to calculate the mass of “Object X” from the orbit of its moon—whose orbital radius (r) is 64,780 kilometers and whose orbital period (P) is 38.200 days—and knowing that the gravitational constant G= 6.673×〖10〗^(-11) m^3 〖kg〗^(-1) s^(-2)(where m= meters, kg= kilograms, and s=seconds).
Express the answer in units of Earth Mass (M_Earth), knowing that M_Earth= 5.980×〖10〗^24 kg.
(Hint: first express r and p in standard units: meters and seconds.)
Given: M=(4π^2 r^3)/(GP^2 ) is known as Kepler’s Third Law where P is the orbital period, r is the orbital radius, and G is the gravitational constant. When given this type of problem, it is important to first understand what it is asking. Identifying what it is asking helps prevent doing more work than necessary and helps in getting the correct answer. First, the question asks us to calculate the mass of Object X. The question also asks to express the answer in units of Earth mass (M_Earth). Therefore, we will have two answers.
Next we identify the variables given in the question. The variables given are: 64,780 kilometers (km) which is the orbital radius (r), 38.200 days which is the orbital radius, and
For instance, you have just calculate the mass of Object X using three values: the gravitational constant, the orbital radius and the orbital period. That’s pretty amazing, especially considering the fact that there aren’t many ways to calculate the mass of an object that is billions of light years away. For example, you cannot simply find a balance or electric scale and find the mass. Furthermore, knowing something, such as the mass, about an object in outer space that we don’t fully understand is in itself quite amazing. So, do consider what you have done, instead of just blindly working through the