Can an Alien See Earth and Venus at the Same Time? | Vectors and Angles Homework

In summary, the question asks if an average one-eyed alien on a spaceship can see Earth and Venus at the same time, given that the direction of Earth is (1,-8,-4), the direction of Venus is (3,12,4), and the average alien eye has a field of view of 5pi/6 radians. The solution involves finding the dot product of the two vectors, which gives a value that suggests an obtuse angle between them. However, this does not provide a definitive answer as the cosine of the angle must be between -1 and 1. Using the exact angle of 5pi/6 radians, which is equivalent to -root(3)/2, also does not help in answering the question
  • #1
nothingsus
16
0

Homework Statement


From an alien spaceship Earth is in the direction (1, -8, -4) and Venus is in the direction (3, 12, 4). The average alien eye has a field of view of 5pi/6 radians. Without using arccos or calculating any exact angles, determine if the average one eyed alien on the spaceship could see Earth and Venus at the same time. You may find it useful to use root(3)/2 approx equal to 0.866

Homework Equations



cos(Θ) = u . v / ||u|| ||v||

The Attempt at a Solution



if i find the dot product of the two vectors, it gives me -109, indicating that the angle between the two vectors is obtuse, however this might still mean that it is greater than 5pi/6 radians.

and now I'm stuck. The above formula tells me that the cos of the angle between the two vectors is -4.95, and using exact angles (which I know I can't do) cos(5pi/6) is -root(3)/2, but I don't know how to use all of this to answer the question
 
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  • #2
nothingsus said:

Homework Statement


From an alien spaceship Earth is in the direction (1, -8, -4) and Venus is in the direction (3, 12, 4). The average alien eye has a field of view of 5pi/6 radians. Without using arccos or calculating any exact angles, determine if the average one eyed alien on the spaceship could see Earth and Venus at the same time. You may find it useful to use root(3)/2 approx equal to 0.866


Homework Equations



cos(Θ) = u . v / ||u|| ||v||

The Attempt at a Solution



if i find the dot product of the two vectors, it gives me -109, indicating that the angle between the two vectors is obtuse, however this might still mean that it is greater than 5pi/6 radians.

and now I'm stuck. The above formula tells me that the cos of the angle between the two vectors is -4.95
? You know that's impossible, don't you? The cosine of any angle must lie between -1 and 1. You have an error somewhere.

, and using exact angles (which I know I can't do) cos(5pi/6) is -root(3)/2, but I don't know how to use all of this to answer the question
 

1. Can an alien actually see Earth and Venus at the same time from their planet?

It is possible for an alien on a distant planet to see both Earth and Venus at the same time, however, it would depend on the location and positioning of their planet in relation to ours. If their planet is in a different orbit, they may not be able to see both Earth and Venus in the night sky simultaneously.

2. How far apart are Earth and Venus from each other in terms of distance?

The average distance between Earth and Venus is approximately 25 million miles, or 40 million kilometers. However, their distance from each other can vary greatly depending on their positions in their respective orbits.

3. What are the chances of an alien actually seeing Earth and Venus at the same time?

The chances of an alien seeing both Earth and Venus at the same time would depend on many factors, such as the distance between our planets, the size and brightness of Earth and Venus in their view, and the location and visibility of their planet in relation to ours. It is difficult to determine the exact chances, but it is possible that some aliens may have seen both planets at the same time.

4. Are there other planets besides Earth and Venus that an alien could potentially see at the same time?

Yes, there are many other planets in our solar system that an alien could potentially see at the same time as Earth and Venus. Depending on their location and positioning, they may be able to see multiple planets in the night sky, including Mars, Jupiter, Saturn, and even Neptune.

5. How do vectors and angles play a role in an alien seeing Earth and Venus at the same time?

Vectors and angles are mathematical concepts that can help us understand the positioning and movements of objects in space. In the case of an alien seeing Earth and Venus at the same time, vectors and angles would be used to calculate the distance between the two planets, as well as the angles at which they are visible from the alien's perspective.

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