Why Does the Equation mg = mv^2/r Work for Calculating Satellite Altitude?

[ys2050]

A remote-sensing satellite travels in a circular orbit at a constant speed of 8.2x10^3m/s. Determine the altitude above Earth's surface.

I thought that I should do GMm/r^2 = mv^2/r and solve for r
but if I do it that way i get a wrong answer.
Instead, if I do mg = mv/r^2 and find r, I get the right answer...
For all the other questions involving satellites and space telescopes and stuff, I always used GMm/r^2 somehow... but how come i just use mg for this question?

Thanks for you help! :)

 

[dynamicsolo]

A remote-sensing satellite travels in a circular orbit at a constant speed of 8.2x10^3m/s. Determine the altitude above Earth's surface.

Sounds like numerical coincidence to me. Read the question you are to answer again. The equation you used,

GMm/r^2 = mv^2/r ,

is correct. However, this will give you the radius of the satellite's orbit. They asked for the altitude of the satellite, so you have to subtract one Earth radius from your answer. (The radius of the orbit is measured from the center of Earth, while the altitude is measured from its surface.)

I will give you the standard warning that this is a favorite "dirty trick" used on exams, particularly in multiple choice questions (including the SAT, GRE, AP Physics, etc.).

 

[Moetasim]

I understand your confusion about using different equations and methods to solve for the altitude of the orbiting satellite. It is important to note that the equations and methods used in physics are dependent on the specific scenario and the variables involved. In this case, the remote-sensing satellite is traveling in a circular orbit, which means it is experiencing a centripetal force towards the center of the orbit. This force is provided by the gravitational force between the satellite and the Earth.

When using the equation GMm/r^2 = mv^2/r, we are equating the centripetal force (GMm/r^2) with the force required to maintain a circular orbit (mv^2/r). However, in this scenario, we do not have the mass of the satellite (m) or the radius of the orbit (r) given. This is why when you solve for r using this equation, you get the wrong answer.

On the other hand, when using the equation mg = mv/r^2, we are equating the weight of the satellite (mg) with the force required to maintain a circular orbit (mv/r^2). In this case, we do not need to know the mass of the satellite or the radius of the orbit, as we can use the acceleration due to gravity (g) and the speed of the satellite (v) to solve for the altitude (r). This method is more appropriate for this scenario as it only involves variables that are given in the question.

In summary, it is important to carefully consider the variables and equations involved in a physics problem and choose the most appropriate method to solve for the desired quantity. I hope this explanation helps to clarify your doubts. Keep up the good work in your studies!