Convert 0.001 arcseconds to radians.

In summary, to convert 0.001 arcseconds to radians, the correct solution is 4.85 x 10^-9 radians. This can be achieved by setting the calculator to radian mode and using the equation (2∏ / (360x60x60)) x 0.001. Alternatively, Google can also be used to calculate the conversion.
  • #1
ZedCar
354
1

Homework Statement



Convert 0.001 arcseconds to radians.

I believe the correct solution is 4.85 x 10^-9 radians.

Homework Equations



2∏rad = 360° = 60' = 3600''

The Attempt at a Solution



The way I was trying to achieve this solution is by setting my calculator to radian mode, typing in {2Pi/(60x60)} x 0.001 which gives 1.74x10^-6.

So I was wondering what I'm doing wrong?

Thank you!
 
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  • #2
2π radians = 360 degrees
1 degree = 60 arcminutes
1 arcminute = 60 arcseconds
 
  • #3
Doc Al said:
2π radians = 360 degrees
1 degree = 60 arcminutes
1 arcminute = 60 arcseconds

That's great. Thanks very much.

(2∏ / (360x60x60)) x 0.001 = 4.85x10^-9
 
  • #5


Your calculation is correct, but you have to remember that 0.001 arcseconds is a very small unit of measurement. It is equivalent to 1/3600000 of a degree, which is why the resulting value in radians is also very small (1.74x10^-6). However, the correct solution is actually 4.85 x 10^-9 radians, as you mentioned in your initial response. This is because 1 arcsecond is equal to 4.85 x 10^-6 radians, and 0.001 arcseconds is 1/1000 of 1 arcsecond. Therefore, to convert 0.001 arcseconds to radians, you simply need to divide 4.85 x 10^-6 by 1000, which gives you 4.85 x 10^-9 radians.
 

FAQ: Convert 0.001 arcseconds to radians.

What is the conversion rate for arcseconds to radians?

1 arcsecond is equivalent to 4.8481 x 10^-6 radians.

2. How do I convert 0.001 arcseconds to radians?

To convert 0.001 arcseconds to radians, multiply 0.001 by 4.8481 x 10^-6. The result is 4.8481 x 10^-9 radians.

3. Why do we need to convert arcseconds to radians?

Radians are the standard unit of measurement for angles in mathematics and physics. Converting from other units, such as arcseconds, allows for consistency and accuracy in calculations.

4. Is there a formula for converting arcseconds to radians?

Yes, the formula is: radians = arcseconds x 4.8481 x 10^-6.

5. Can you provide a real-life example of converting arcseconds to radians?

One example is in astronomy, where arcseconds are used to measure the apparent size of celestial objects. Converting these measurements to radians allows for more precise calculations in determining distances and sizes of objects in space.

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