How Do You Calculate the Velocity of a Comet at Different Points in Its Orbit?

[fball558]

Velocity of coment?? help please

Homework Statement

A certain comet of mass m at its closest approach to the Sun is observed to be at a distance r1 from the center of the Sun, moving with speed v1. At a later time the comet is observed to be at a distance r2 from the center of the Sun, and the angle between r2 and the velocity vector is measured to be θ. What is v2? For example, if a variable g is used in the question, type g. Use theta for θ, r_1 for r1, r_2 for r2, v_1 for v1 and m as needed.

pic is attached so you can see what I am looking at as well.

im completely stuck don't even know where to begin!

 

[tiny-tim]

Hi fball558!

(eughh … why is v1 in your diagram pointing up? :yuck:)

Hint: conservation of … ?

 

[nlightner]

I would first start by identifying the relevant equations and principles that can help us solve this problem. In this case, we can use the conservation of angular momentum and the law of gravitation.

The conservation of angular momentum states that the angular momentum of a system remains constant as long as there is no external torque acting on it. In this case, the comet is moving in an elliptical orbit around the Sun, and the force of gravity is the only external force acting on it. Therefore, we can use the conservation of angular momentum to relate the comet's speed at different points in its orbit.

The law of gravitation states that the force of gravity between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. In this case, we can use this law to relate the comet's distance from the Sun to its speed.

Using these principles, we can set up the following equation:

mvr = mvr1

Where m is the mass of the comet, v is its velocity at a specific point in its orbit, and r is its distance from the Sun. We can rearrange this equation to solve for v:

v = (r1/r) * v1

Next, we can use the law of gravitation to relate the comet's distance from the Sun to the force of gravity acting on it:

F = GmM/r^2

Where G is the gravitational constant, M is the mass of the Sun, and r is the distance between the comet and the Sun. We can also relate the force of gravity to the acceleration of the comet using Newton's second law:

F = ma

Combining these equations and solving for v, we get:

v2 = √[GM(2/r2 - 1/r1)]

Where G is the gravitational constant, M is the mass of the Sun, r1 is the distance of the comet at its closest approach to the Sun, and r2 is the distance of the comet at a later time.

Therefore, the velocity of the comet at a later time (v2) can be calculated using the mass of the comet (m), the distance at its closest approach (r1), and the distance at a later time (r2).

I hope this helps!