Circular Motion and Gravitation questions

[Numbnut247]

Hey guys, I have a few Circular Motion and Gravitation questions that I have almost no idea how to do:

1. The orbital radius of Mars around the Sun is 1.52 times that of Earth's orbital radius (1.50 X 10^11m). In Earth years, what is the period of revolution for Mars in this orbit? (I need to know how to solve this question.)

My work:

4((3.14)^2)(r)/(8.61 X 10^4)^2 = 4((3.14)^2)(1.52)/T^2
and solve for T (Sorry for the messy numbers. )

However, I have no idea if that is even close of what I should be doing.

2. Two satellites, X and Y, are placed in orbit around a planet. Satellite X has a period of revolution of 3.6 X 10^5 s and an orbital radius of 7.5 X 10^8 m. If the orbital radius of satellite Y is 3.0 X 10^9 m, what is its orbital period?

I have no idea how to approach this question.

3. For gravitation and circular motion of planets and large masses, is the centripetal force equal to the gravitational force of attraction?

Thank you very much guys

Edit: Finally, is the period how long it takes for something to have 1 revolution, and the frequency is the number of revolutions per 1 second? Thanks again.

 

[Andrew Mason]

Hey guys, I have a few Circular Motion and Gravitation questions that I have almost no idea how to do:

1. The orbital radius of Mars around the Sun is 1.52 times that of Earth's orbital radius (1.50 X 10^11m). In Earth years, what is the period of revolution for Mars in this orbit? (I need to know how to solve this question.)

My work:

4((3.14)^2)(r)/(8.61 X 10^4)^2 = 4((3.14)^2)(1.52)/T^2
and solve for T (Sorry for the messy numbers. )

Suggestion: Find the algebraic solution and use arithmetic to work out the answer.

What is the relationship between period and radius? (Think of the force of gravity supplying the centripetal force).

2. Two satellites, X and Y, are placed in orbit around a planet. Satellite X has a period of revolution of 3.6 X 10^5 s and an orbital radius of 7.5 X 10^8 m. If the orbital radius of satellite Y is 3.0 X 10^9 m, what is its orbital period?

Again, think of the force of gravity supplying the centripetal force. What is the expression for centripetal force? What is the expression for the force of gravity? Figure out the Mass of the planet from the period and radius of X's orbit. Then figure out the orbital period Y from that.

3. For gravitation and circular motion of planets and large masses, is the centripetal force equal to the gravitational force of attraction?

What is the acceleration of the planet? What supplies it? Is there any other force other than gravity acting on the planet?

Edit: Finally, is the period how long it takes for something to have 1 revolution, and the frequency is the number of revolutions per 1 second?

Yes.

AM

 

[Numbnut247]

Thank you so much

I have one last question (PROMISE):

A person is on a horizontal rotating platform at a distance of 4.3m from the its centre. This person experiences a centripetal acceleration of 5.6m/s^2. What centripetal acceleration is experienced by another person who is at a distance of 2.5m from the centre of the platform?

How do I got about doing this question? Can I assume the velocity for the 2 people are the same? I figured out the velocity of the 1st person, but do I assume that the velocity is the same for the other person? Or do I assume the period is the same for the 2 people?

Thanks a ton!

 

[Andrew Mason]

Thank you so much

I have one last question (PROMISE):

A person is on a horizontal rotating platform at a distance of 4.3m from the its centre. This person experiences a centripetal acceleration of 5.6m/s^2. What centripetal acceleration is experienced by another person who is at a distance of 2.5m from the centre of the platform?

How do I got about doing this question? Can I assume the velocity for the 2 people are the same? I figured out the velocity of the 1st person, but do I assume that the velocity is the same for the other person? Or do I assume the period is the same for the 2 people?

You don't have to assume anything. You are given sufficient information.

How could the rotation period of a person who is stationary with respect to the platform be any different than the period of rotation of the platform itself? What is the expression for velocity? Angular velocity? Which of those depend on the distance from the centre?

AM