# Period of Revolutions of a Planet

• shanklove
In summary, a neutron star with a radius of 10,000 km and a planet with a period of 30 days will experience a change in period for the planet when the star collapses to a radius of 3 km. Using the conservation of angular momentum, the new period of revolution for the planet can be calculated by multiplying the initial period by the ratio of the final and initial radii squared.
shanklove

## Homework Statement

A neutron star has a radius of 10,000 km, and takes a planet 30 days to complete one revolution around the star. When the star collapses, the new radius is 3 km. Find the new period of revolution of the newly formed neutron star.

## Homework Equations

T=2(pi)/omega
omega = (v cross r)/r^2

## The Attempt at a Solution

Not sure even how to approach this. I'm so confused and i can't find the velocity to find omega! this is my first post on PF, any help please?!

shanklove said:

## Homework Statement

A neutron star has a radius of 10,000 km, and takes a planet 30 days to complete one revolution around the star. When the star collapses, the new radius is 3 km. Find the new period of revolution of the newly formed neutron star.

## Homework Equations

T=2(pi)/omega
omega = (v cross r)/r^2

## The Attempt at a Solution

Not sure even how to approach this. I'm so confused and i can't find the velocity to find omega! this is my first post on PF, any help please?!

Are you doing Kepler's Laws? The relationship between period and radius, one squared and the other cubed. Or is your class studying some other subject? And are you asking about the new period of the planet or the neutron star... something seems missing or stated slightly skewed...

pgardn said:
Are you doing Kepler's Laws? The relationship between period and radius, one squared and the other cubed. Or is your class studying some other subject? And are you asking about the new period of the planet or the neutron star... something seems missing or stated slightly skewed...

We're doing oscillatory motion and rotational motion and angular momentum. Oh and I'm assuming that he was asking for the period of the planet, the period of the star wouldn't make sense.

The collapse has no effect on the orbit of the planet (that will probably be the next question)
For the star you just need conservation of angular momentum.
Whats the angular momentum of a uniform sphere?

Have you done the conservation of angular momentum?

mgb_phys said:
The collapse has no effect on the orbit of the planet (that will probably be the next question)
For the star you just need conservation of angular momentum.
Whats the angular momentum of a uniform sphere?

It's just 2pi/T. So would it be 2pi/2592000?

Angular momentum is = I * rotation rate
Where I depends on the shape but for a sphere it is proportional to r^2
(http://en.wikipedia.org/wiki/List_of_moments_of_inertia)

So if you make r half as much the moment of intertia becomes 4x smaller, since the angular momentum is the same then it must go 4x faster.

How much is r reduced in this case?

Not following...

From your link I= (2mr^2)/5 <----assuming you mean I= moment of inertia. But it would make more sense to me that I=r^2. So what do I do now with the rotational rate...? I'm so confused =X

Ok I think I got it!

I(initial)*Omega(initial)=I(final)*Omega(final)

So I(initial)*(2pi/T(initial)) = I(final)*(2pi/T(final))

If the distribution is symmetric then kMR(initial)^2*(I(initial))=kMR(final)^2*(I(final))

So the kMR would cancel out on each side, so it would have Ri^2*(2pi/Ti)=Rf^2*(2pi/Tf)

Divide 2pi/Ti on each side and then divide by Ri. Multiply Tf on the other side and you get:

Tf = (Rf/Ri)^2 * Ti

Plug in and solve.

I feel smart now =)

## What is the period of revolution of a planet?

The period of revolution of a planet is the amount of time it takes for the planet to complete one orbit around its star. This is also known as the planet's year.

## How is the period of revolution calculated?

The period of revolution can be calculated using Kepler's third law of planetary motion, which states that the square of a planet's orbital period is proportional to the cube of its semi-major axis (the average distance between the planet and its star).

## What factors can affect the period of revolution of a planet?

The period of revolution can be influenced by the mass of the planet, the mass of its star, and the distance between the planet and its star. Additionally, the presence of other planets in the same system can also affect the period of revolution through gravitational interactions.

## Why is the period of revolution important to study?

The period of revolution is important to study because it provides valuable information about the characteristics of a planet and its orbit. It can also help us understand the dynamics of a planetary system and how it evolves over time.

## How do scientists measure the period of revolution of a planet?

Scientists can measure the period of revolution of a planet using various methods such as observing the planet's transit across its star, measuring the Doppler shift of the star's light caused by the planet's gravitational pull, or using direct imaging techniques.

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