Physics circular motion, orbits, and gravity

[thesandalman]

Homework Statement

ics
Consider identical twins named Bert and Ernie who are visiting a star named Alpha Sesame. Bert is at a distance r from the star while Ernie is located a distance 3r. Both Bert and Ernie are stationary (they are standing on platforms built by an alien super race) and are not orbiting the star. Big Bird, who has the same mass as Bert and Ernie despite his larger volume, flies by Bert in a spaceship which is in a circular orbit or radius r around Alpha Sesame.

All Answers are true or false:

-If Bert and Ernie would step on bathroom scales, Bert's weight would be 9 times larger than Ernie's.
-If Bert were to step off the platform and fall toward the star, he would experience an identical acceleration to that of Big Bird.
-If Big Bird were to step on a bathroom scale in the spaceship, the scale would register zero.
-Big Bird's acceleration is zero.
-The gravitational force that Bert feels is 3 times larger than the gravitational force Ernie feels.

Homework Equations

The Attempt at a Solution

I know the third answer to be true. I believe the fourth question is false due to gravity. Not so sure about the other ones. That is where I need the help!

 

[wwshr87]

For this question you need to look at Newton's law of universal gravitation,
F=(Gm1m2)/r^2. Also, take a look at centripetal force, F=(m*V^2)/R.
That should get you started.

 

[thesandalman]

Ok, here is what I am thinking:
Question 1 is true due to the fact that force is 1/9 or therefore 9 times the weight. Question 2 i also say is true because the same force would be acting on both big bird in orbit and Burt when he falls off the platform.
Question 3 I know is true because they are in the equlibrium.
Question 4 is False due to gravity.
Question 5 is true due to this equation F=(Gm1m2)/r^2.

Am I on the right track?

 

[wwshr87]

I agree with your answer for question number one, since the relation between the distances is squared. Question two seems ok also. I don’t understand question 3.
Number four is correct there is an acceleration. I don’t agree with number 5 because if you look at F=(Gm1m2)/r^2, Bert feels a gravitational force 9 times greater, the term in r^2.

 

[thesandalman]

Thanks you so very much for your help! I really appreciate it! You were correct by the way.