How big is the comet based on a 735x731px surface picture taken from 3km away?

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In summary, the conversation discusses the calculation of the width of a comet based on a picture with a resolution of 3.5 times lower than Tycho Brache's. The picture is 735x731px and taken from a probe 3 kilometers away from the comet. By using the equation α=l/r, where α is the angle, l is the arc, and r is the distance, it is determined that each pixel represents an angular size of 3.5 arc minutes. With this information, the linear size of each pixel can be calculated and used to find the width of the comet. However, the calculations must be done in radians to get an accurate result.
  • #1
member578757

Homework Statement


There is a picture, size 735x731px, that show the surface of comet that was taken from a probe distanced 3 kilometers from the comet. If the resolution of the camera that recorded the surface is 3.5 times lower then the resolution of Tycho Brache (that is 1 angular minute, 1/60 of a degree), what is the width of the comet? Use expresion for α (angle), arch (l) and distance (r)

Homework Equations


α=l/r
l=α*r

The Attempt at a Solution


l=(3.5/60)*3000meters
l=175meters
To me this seems to small, the comet is like 2,2km wide or more. Also I have no idea in what way to use the pixels to calculate the right size.
Any help would be nice
 
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  • #2
Hi Boxblax, Welcome to Physics Forums.

Boxblax said:

Homework Statement


There is a picture, size 735x731px, that show the surface of comet that was taken from a probe distanced 3 kilometers from the comet. If the resolution of the camera that recorded the surface is 3.5 times lower then the resolution of Tycho Brache (that is 1 angular minute, 1/60 of a degree), what is the width of the comet? Use expresion for α (angle), arch (l) and distance (r)

Homework Equations


α=l/r
l=α*r

The Attempt at a Solution


l=(3.5/60)*3000meters
l=175meters
To me this seems to small, the comet is like 2,2km wide or more. Also I have no idea in what way to use the pixels to calculate the right size.
Any help would be nice
Wouldn't the resolution information imply that each image pixel represents angular size of 3.5 arc minutes? How many pixels across is the picture?
 
  • #3
It is 731px across. Could you please explain more how to solve it
 
  • #4
If each pixel represents an angular size of 3.5 arc minutes, the what linear size does each pixel represent at 3 km distance?
 
  • #5
Yes, that is what i need to find out. I need to find out the real size of comet. How to find out the size of 1 pixel in meters?
 
  • #6
Boxblax said:
Yes, that is what i need to find out. I need to find out the real size of comet. How to find out the size of 1 pixel in meters?
Draw it out. You have an angle of 3.5 arc minutes and a range of 3 km. What's the length of the arc on the end of that radius? Look at your Relevant equations.
 
  • #7
175meters? I don't quite understand what you want to do. Could you solve it?
 
  • #8
Helpers are not allowed to solve homework problems for you. We can only provide hints and suggestions, or point out errors. It's in the forum rules (which you read right? :smile:).

175 meters is not correct. One pixel spans an angle of 3.5 arc minutes. That's 3.5 x (1/60) degrees. With a radius of 3 km, what is the length of the arc that is swept out by that angle? Show your calculations.
 
  • #9
my calculations are in a photo. still doesn't seem right to me, maybe i am wrong
 

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  • #10
Remember that geometrical calculations involving angles should use radians. Otherwise, you can approximate the figure with a right angle triangle since the radius is so large, and use the tangent function.

I'd convert the angle in arcminutes to radians in your calculation.
 
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  • #11
thanks mate
 

1. How do scientists calculate the size of a comet?

Scientists use various methods, such as measuring the brightness of the comet's nucleus and its surrounding coma, to estimate the size of a comet. They also use radar measurements and spectrometry to gather data on the comet's size and composition.

2. What is the average size of a comet?

The average size of a comet varies greatly, but most comets have a nucleus ranging from a few hundred meters to a few kilometers in diameter. However, some comets can have much larger nuclei, up to tens of kilometers in diameter.

3. Can the size of a comet change over time?

Yes, the size of a comet can change over time due to various factors, such as sublimation of ice and dust from the nucleus, collisions with other objects, and outgassing from the comet's surface. These changes can be observed and measured by scientists.

4. How do scientists measure the size of a comet from Earth?

Scientists use telescopes equipped with various instruments, such as cameras and spectrometers, to gather data on the size and composition of a comet. They also use mathematical models and calculations to estimate the size of a comet based on its observed properties.

5. Why is it important to know the size of a comet?

Knowing the size of a comet can provide valuable information about its composition, structure, and behavior. This can help scientists better understand the formation and evolution of comets, as well as their potential impact on Earth. Additionally, studying the sizes of different comets can provide insights into the diversity of objects in our solar system.

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