Planet Velocity at Aphelion: Find the Answer

In summary, a planet's velocity at aphelion is its speed at the point in its orbit farthest from the sun, and can be calculated using the formula v = √(GM(2/r - 1/a)). This velocity is affected by the mass of the sun, distance from the sun at aphelion, and the shape of the planet's orbit. Knowing a planet's velocity at aphelion is important for understanding its motion and predicting future positions, and it can change over time due to various factors.
  • #1
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Homework Statement



At perihelion a planet in another solary system is 175 x 10 ^ 6km from its Sun and is traveling at 40km/s. At aphelion it 250 x 10 ^ 6 km distant and is traveling at?

Homework Equations




IiWi = IfWf

The Attempt at a Solution



What do i do?
 
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  • #2
Use conservation of angular momentum as you are trying to do. What are I and W in terms of mass m, velocity v and radius r of the planet?
 
  • #3


To find the velocity at aphelion, we can use the equation for conservation of angular momentum, IiWi = IfWf, where I is the moment of inertia and W is the angular velocity. Since the distance from the Sun changes at aphelion and perihelion, we can assume that the moment of inertia also changes. However, since the mass of the planet remains constant, the angular momentum must also remain constant. Therefore, we can set IiWi = IfWf and solve for Wf using the given values for Ii, Wi, and If. This will give us the velocity at aphelion. We can also use the formula for orbital velocity, v = √(GM/r), where G is the gravitational constant, M is the mass of the sun, and r is the distance from the sun, to calculate the velocity at aphelion. We can plug in the values for M and r at aphelion and solve for v. Both methods should give us the same answer for the velocity at aphelion.
 

1. What is a planet's velocity at aphelion?

A planet's velocity at aphelion is its speed at the point in its orbit where it is farthest from the sun. This is also known as the planet's maximum orbital velocity.

2. How is a planet's velocity at aphelion calculated?

A planet's velocity at aphelion can be calculated using the formula v = √(GM(2/r - 1/a)), where v is the velocity, G is the gravitational constant, M is the mass of the sun, r is the distance from the planet to the sun at aphelion, and a is the semi-major axis of the planet's orbit.

3. What factors affect a planet's velocity at aphelion?

A planet's velocity at aphelion is affected by the mass of the sun, the distance between the planet and the sun at aphelion, and the shape of the planet's orbit. The more massive the sun and the farther the planet is from it at aphelion, the higher the velocity will be.

4. Why is it important to know a planet's velocity at aphelion?

Knowing a planet's velocity at aphelion is important for understanding its motion and behavior in its orbit. It can also help in predicting future positions of the planet and determining its overall orbital stability.

5. Can a planet's velocity at aphelion change over time?

Yes, a planet's velocity at aphelion can change over time due to various factors such as gravitational interactions with other objects, changes in the shape of its orbit, and the influence of other forces like radiation pressure.

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