Solid Angle of Moon: How Far for Dime to Appear Same Size?

In summary, the question is asking how far a dime must be held from your face in order for it to appear the same size as the Moon, given a distance to the Moon of 384,400 km and a radius of 1738 km. The suggested approach is to find the solid angle of the Moon as seen from Earth, and then use the equation dω = sin θ dθ dφ to solve for the distance.
  • #1
AnthonyS
2
0

Homework Statement



How many inches from your face would you have to hold a dime in order for it to appear the exact same size as the Moon? Use a distance to the Moon of 384,400 km and a radius of the Moon of 1738 km. The diameter of a dime is 17.1 mm. (Hint: Find at what distance a dime has the same solid angle as the Moon).

Homework Equations



dω = sin θ dθ dφ

The Attempt at a Solution



This is for my Physics of Meteorology class. I am trying to find the solid angle of the moon as seen from Earth first, and then will attempt the rest. I have thus far, ω=[tex]\int\int[/tex]sin θ dθ dφ, where the first integral goes from 0 to 2pi and the second from 0 to θ, but I'm lost as to how to solve it.

Anthony
 
Physics news on Phys.org

1. What is the solid angle of the moon?

The solid angle of the moon refers to the amount of space that is subtended by the moon as seen from a certain point. It is measured in steradians (sr) and is equal to the area of the moon's surface divided by the square of the distance from the observer to the moon.

2. How is the solid angle of the moon related to its size?

The solid angle of the moon is directly proportional to its size. This means that as the size of the moon increases, so does its solid angle. However, the distance between the observer and the moon also plays a role in determining the solid angle.

3. How far does the moon need to be for a dime to appear the same size?

This distance can vary depending on the size of the dime and the angle at which it is viewed. On average, the moon would need to be approximately 238,855 miles away for a US dime (17.91mm in diameter) to appear the same size as the moon's solid angle.

4. Why does the moon appear the same size as a dime at a certain distance?

This is due to the concept of angular size, which is the perceived size of an object based on its angular diameter. The moon and a dime may have vastly different physical sizes, but when viewed from a certain distance, their angular sizes are similar and thus they appear to be the same size.

5. Is the solid angle of the moon constant?

No, the solid angle of the moon is not constant. It changes as the moon orbits around the Earth, resulting in variations in its distance from the observer. Additionally, atmospheric conditions and the angle at which the moon is viewed can also affect its perceived solid angle.

Similar threads

Stephan-Boltzmann law, solid angle integral, and an extra pi factor
    • Advanced Physics Homework Help
Replies
1
Views
2K
Projectile Motion on the Moon: Finding the Optimal Launch Angle Using Equations
    • Introductory Physics Homework Help
Replies
2
Views
2K
Calculating steradians (solid angle)
    • Calculus and Beyond Homework Help
Replies
4
Views
3K
Phase space of spherical coordinates and momenta
    • Advanced Physics Homework Help
Replies
9
Views
5K
I How Big of an Object Orbiting Closer to the Sun Than Earth Could Be Overlooked?
    • Astronomy and Astrophysics
Replies
17
Views
2K
Rate of Change of Angle for 90 ft Wire Attachment
    • Calculus and Beyond Homework Help
Replies
14
Views
3K
Why Does cos(x)^2 Average to 1/3 Over a Sphere's Solid Angle?
    • Advanced Physics Homework Help
Replies
4
Views
16K
Understand Effusion of a Gas: Speed & Angle Distribution
    • Introductory Physics Homework Help
Replies
6
Views
2K
Help with magnetic field in sphere problem
    • Advanced Physics Homework Help
Replies
1
Views
2K
Integral of differential cross section over solid angle
    • Calculus and Beyond Homework Help
Replies
5
Views
4K

Hot Threads

Recent Insights

Back
Top