# Comet on a parabolic orbit around the Sun

• math 2015
In summary, the homework problem is asking for the comet's full energy and distance from the sun at perihelion, as well as the time spent within Earth's orbit. The equation for parabolic orbit and specific mechanical energy are relevant to solving this problem. Hard data, such as the speed at perihelion, is needed in order to solve for the time spent within Earth's orbit.
math 2015

## Homework Statement

given: the speed at perihelion

What is comets full energy? What is its distance from Sun at perihelion?
How much time is the comet located inside Earth's orbit?

## Homework Equations

parabolic orbit equation

3. The attempt at a solutin
wrongly calculated l

$$r(\theta) = \frac{L^2}{GMm^3}\,\frac{1}{1+\epsilon\,\cos{\theta}}$$
L is constant, so the same for every ##\theta##. Take an easy value.

math 2015 said:

## Homework Statement

given: the speed at perihelion

What is comets full energy? What is its distance from Sun at perihelion?
How much time is the comet located inside Earth's orbit?
You're first asked about the "full energy" of the of the comet's orbit. Presumably that's the mechanical energy. What is the expression for the specific mechanical energy (ξ) of an orbit? What is its value for any parabolic orbit?

In order to answer the part about the time spent within the Earth's orbit you will need some hard data. Are you given an actual value for the speed at perihelion?

94 km/s

math 2015 said:
94 km/s
Okay, now you'll have to show some details of your efforts so far to answer the given problem.

@math 2015 I'm closing this thread since you haven't shown any effort. If you wish to continue, contact me or begin a new thread showing your attempt in detail.

## 1. What is a parabolic orbit?

A parabolic orbit is a type of trajectory that is followed by an object as it moves around a central body, such as the Sun. It is characterized by a shape that resembles a stretched out letter 'U' and is often described as being halfway between a circular and a hyperbolic orbit.

## 2. How does a comet follow a parabolic orbit around the Sun?

A comet follows a parabolic orbit around the Sun when it is traveling at a high enough velocity to escape the gravitational pull of the Sun, but not enough to leave the solar system completely. This allows the comet to continuously loop around the Sun in a parabolic path.

## 3. What determines the shape and size of a comet's parabolic orbit?

The shape and size of a comet's parabolic orbit is determined by its initial velocity and the gravitational pull of the Sun. Comets with higher initial velocities will have larger and more elongated orbits, while those with lower velocities will have smaller and more circular orbits.

## 4. How long does it take for a comet to complete a parabolic orbit around the Sun?

The time it takes for a comet to complete a parabolic orbit around the Sun can vary depending on its distance from the Sun and its velocity. On average, it can take anywhere from a few years to a few decades for a comet to complete one full orbit.

## 5. What happens to a comet's orbit if it gets too close to the Sun?

If a comet gets too close to the Sun, it can be affected by its immense gravitational pull. This can cause the comet's orbit to become more elliptical or even change to a hyperbolic orbit, which would result in the comet leaving the solar system entirely.

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