Kinematic Distance Problem? Can't Tell

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In summary, the problem is to find the diameter of the moon given its distance from Earth and the angle it subtends from an observer's perspective. It involves using trigonometry to calculate the height of a triangle with known angle and distance, and then finding the diameter using the relationship between the height and diameter of a circle. The expected result is around 3100 km or 1500 miles, which is approximately 4 times less than the diameter of Earth.
  • #1
adk
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Homework Statement


An observer on the Earth observes the angle subtended by the diameter of the moon to be 0.009199 radians. If the moon is 234,800 miles away, what is its diameter?

Homework Equations





The Attempt at a Solution


Not quite sure where to begin with this one. I think it may be a kinematics distance problem but not 100% sure. Suggestions?
 
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  • #2
This is a common trigonometry problem.

Go from there.
 
  • #3
Btw the result must be somewhere around 4 times less than the Earth's so around 3100 km or 1500 miles.
 
  • #4
still not sure where to begin as far as equations go.

how do we know it will be 4 times less than the earth?
 
  • #5
adk said:
still not sure where to begin as far as equations go.

how do we know it will be 4 times less than the earth?

This is general knoledge.

Imagine a triangle with one point the observer, and the other the poles of the moon, you have one angle and a distance which is the height of the trianlge in the Observers point...
 

1. What is the Kinematic Distance Problem?

The Kinematic Distance Problem is a concept in astrophysics that involves determining the distance to an object in space using its observed motion and velocity. It is a challenging problem that requires advanced mathematical and computational techniques to solve.

2. How is the Kinematic Distance Problem relevant in astrophysics?

The Kinematic Distance Problem is relevant in astrophysics because it allows scientists to accurately measure the distances of objects in the universe. This is important for understanding the scale and structure of the cosmos, as well as for studying the evolution of galaxies and the expansion of the universe.

3. What are some common methods used to solve the Kinematic Distance Problem?

Some common methods used to solve the Kinematic Distance Problem include the kinematic distance formula, which uses the object's observed radial velocity and proper motion, and the parallax method, which measures the object's apparent shift in position as the Earth orbits the Sun. Other techniques include using standard candles, such as Cepheid variables, and multi-wavelength observations.

4. What are some challenges in solving the Kinematic Distance Problem?

One of the main challenges in solving the Kinematic Distance Problem is the uncertainty in the object's observed motion and velocity. This can be due to various factors such as measurement errors, gravitational interactions with other objects, and the object's intrinsic velocity. Additionally, the complex nature of the problem requires a high level of mathematical and computational skill to accurately calculate the distance.

5. How does solving the Kinematic Distance Problem contribute to our understanding of the universe?

Solving the Kinematic Distance Problem is crucial for understanding the scale and structure of the universe. By accurately measuring the distances of objects, scientists can map out the distribution of matter and study the evolution of galaxies. It also plays a crucial role in determining the expansion rate of the universe and the presence of dark matter and dark energy, which are essential for our understanding of the cosmos.

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