# Stellar aberration with non perpendicular starlight

• Jean-C
In summary, the problem is that we can't solve for the value of theta when the Earth speed and starlight speed are not perpendicular. We use the equation for the major axis, but it doesn't work when the Earth is closer or further from the sun. We can use a reference frame to find where the starlight ends up, but I lost the sketch that I drew.
Jean-C

## Homework Statement

So the problem is the following : we observe the stellar aberration of a star which isn't on the zenith, so that the star forms an angle theta with the ecliptic plane of the Earth. With such a position, the star will describe an ellipse instead of a circle (typical movement for a star at zenith). This is due to the fact that the starlight isn't always perpendicular to the speed vector of the Earth. The task is to find the value of theta knowing that the minor axis value is 36''. We consider Earth speed to be constant.

## Homework Equations

tan(alpha)=v/c when the Earth speed and starlight speed are perpendicular (v is Earth speed)
2*alpha is the axis related to that angle

## The Attempt at a Solution

I've tried different methods but I can't find a way to solve the value of theta. What I know is that the major axis is 2*alpha : when the Earth is nearest to be sun and at the furthest, the speed of Earth and starlight are perpendicular, so we can apply the equation written higher. But for the positions 1/4 of a period later, the starlight and Earth speed aren't perpendicular. One of the speed forms an angle theta with starlight, the angle we are looking for (the other position forms an angle 180-theta, which gives the same sin value).

This is where I block : I can't find a way to link the value of the minor axis to theta, since the above equations apply only when Earth speed and starlight form a right triangle...

Did you draw a sketch? You can use the reference frame of the distant star, and a telescope moving in some direction not perpendicular to the starlight hitting the telescope. Where does the starlight end up?

I had a sketch drawn, but redrew it just in case and found out what I was missing! Thanks for your reply!

## 1. What is stellar aberration with non perpendicular starlight?

Stellar aberration with non perpendicular starlight is a phenomenon that occurs when light from a star is not hitting the observer's eyes at a perfect right angle. This can happen when the observer is moving, causing the starlight to appear shifted in the sky.

## 2. How does stellar aberration with non perpendicular starlight happen?

This phenomenon occurs due to the finite speed of light and the movement of the observer. As the observer moves, the angle at which the light hits their eyes changes, causing the starlight to appear shifted.

## 3. How is stellar aberration with non perpendicular starlight different from regular stellar aberration?

Regular stellar aberration occurs when the observer is moving perpendicular to the direction of the incoming starlight. In contrast, stellar aberration with non perpendicular starlight occurs when the observer is moving at an angle to the incoming starlight.

## 4. What is the significance of studying stellar aberration with non perpendicular starlight?

Studying this phenomenon can help scientists better understand the movement and speed of stars, as well as the properties of light. It can also provide insights into the motion of the observer and the Earth's orbit.

## 5. Can stellar aberration with non perpendicular starlight be observed with the naked eye?

No, this phenomenon is difficult to observe with the naked eye due to the small angle at which the starlight is shifted. It requires precise measurements and specialized equipment to detect and study.

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