# Astronomy - aphelion/perihelion from conservation

• Odyssey
In summary, The person is seeking help in deriving the velocities at perihelion and aphelion using the conservation of specific angular momentum and energy. They are confident in the energy part but need assistance with the specific angular momentum method.
Odyssey
Hi all,

I'm stuck on this question for my assginment...i need to derive the velocity at perhelion and aphelion using two separate methods: the conservation of specific angular momentum and energy.

I think I'm OK with the energy part but I'm stuck on getting the velocities at aphelion and perihelion using the conservation of specific angular momentum. If you guys can help me out it'd be great! Thanks.

Odyssey said:
Hi all,

I'm stuck on this question for my assginment...i need to derive the velocity at perhelion and aphelion using two separate methods: the conservation of specific angular momentum and energy.

I think I'm OK with the energy part but I'm stuck on getting the velocities at aphelion and perihelion using the conservation of specific angular momentum. If you guys can help me out it'd be great! Thanks.
Angular momentum magnitude is just rmv when the velocity is perpendicular to the vector r.

## 1. What is aphelion and perihelion?

Aphelion and perihelion refer to the two extreme points in an orbit of a planet or other celestial body around the sun. Aphelion is the point in the orbit that is farthest from the sun, while perihelion is the point that is closest to the sun.

## 2. How does conservation play a role in aphelion and perihelion?

Conservation laws in astronomy refer to the principles that describe the behavior of celestial bodies in space. In the case of aphelion and perihelion, conservation of angular momentum and conservation of energy play a role in determining the distance of a planet from the sun at these points in its orbit.

## 3. What causes the difference in distance between aphelion and perihelion?

The elliptical shape of a planet's orbit causes the difference in distance between aphelion and perihelion. As a planet moves along its orbit, it is constantly pulled towards the sun by gravity, resulting in a faster speed at perihelion and a slower speed at aphelion.

## 4. How does the distance between aphelion and perihelion affect a planet's temperature?

The distance between aphelion and perihelion plays a significant role in a planet's temperature. At aphelion, a planet is farther from the sun and receives less solar radiation, resulting in cooler temperatures. At perihelion, a planet is closer to the sun and receives more solar radiation, resulting in warmer temperatures.

## 5. How often do aphelion and perihelion occur?

The occurrence of aphelion and perihelion depends on the orbital period of a planet, which is the time it takes for a planet to complete one orbit around the sun. For Earth, aphelion and perihelion occur approximately every 6 months, while for Mars it occurs every 2 years. The exact timing of aphelion and perihelion may also vary slightly due to gravitational interactions with other planets.

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