EK 1001 physics g force satellite in its orbit 209.

[GRod18]

---

Members do not see this ad.

man this was a really difficult problem for me to wrap my brain around.

Gravitational force holds a satellite in its orbit. Which of the following would most likely increase the time necessary for a satellite to complete its orbit around a planet? EK explanation included lots of algebraic steps.

A. decreasing only the orbital radius
B. Increasing only the mass of the satellite
C. Decreasing only the mass of the planet
D. Decreasing only the radius of the planet.

Is there an intuitive way to go about this problem?
*note this is the last question in the section so its difficulty is high and probably not comparable to AAMC tests.

 

[Rabolisk]

I could see this being on the MCAT because it's not a particularly hard question. The answer is C. To increase the time required for orbit, you have to either increase the distance traveled, which is the circumference, or decrease speed. Decreasing speed can be achieved by decreasing the mass of the planet, since that decreases force on the satellite.


Let's look at the other choices. Decreasing orbital radius not only decreases the circumference, but also increases force, thus increasing speed. Clearly the opposite of what we want. Increasing mass of satellite increases force. Speed is unaffected though because force divided by mass is still the same. Finally planet radius has no effect because it is the orbital radius that matters. It doesn't affect force because the satellite is still the same distance away from the center of the planet.

I think knowing the relevant equations and using math is useful. The three relevant equations are the gravitational force between two objects, centripetal force, and definition of period if an orbit. Being mathematically intuitive goes a long way.

 

[IntelInside]

I could see this being on the MCAT because it's not a particularly hard. The answer is B. To increase the time required for orbit, you have to either increase the distance traveled, which is the circumference, or decrease speed. Decreasing speed can be achieved by decreasing the mass of earth, since that decreases force on the satellite.

The answer is C then according to your reasoning which I agree with. I think you just chose the wrong answer choice by accident.

F = Gm1m2/r^2 = m1v^2/r

Therefore decrease mass of planet decrease either v or increase r to accommadate the change. I agree with rabolisk as well that this question isnt hard at all and could def be on the MCAT

 

[GRod18]

I appreciate the prompt response, thank you both!

I like the intuitive thinking, the way EK manipulated the equations to get to the last step 4pi^2r^3 = GMt^2. It just didn't seem to be something I could do under time constraints.