The physical length of the ruler as a fraction of the circumference of the big circle is the same as the angular length of the ruler as a fraction of 360°: length circumference 0 360° Since circumference = 2π X radius and the radius of the big circle is the distance to the ruler/planet: length 2π × distance Ꮎ 360° Solving for the physical length of the ruler yields: length = 2 × distance x 0 360° This general equation can be used along with the distance to your planet to work out a conversion factor that will convert your moon's orbital semi-major axis from arcseconds to AU; i.e. in the above equation, we will set length = a [AU], 0=a"], and calculate conversion factor ["/AU] = 2πT 360° 1° 3600" × distance. conversion factor = type your answer... "/AU. Note: in order for units to work out, we had to multiply by the number of degrees per arcsecond (") in the above formula.
The physical length of the ruler as a fraction of the circumference of the big circle is the same as the angular length of the ruler as a fraction of 360°: length circumference 0 360° Since circumference = 2π X radius and the radius of the big circle is the distance to the ruler/planet: length 2π × distance Ꮎ 360° Solving for the physical length of the ruler yields: length = 2 × distance x 0 360° This general equation can be used along with the distance to your planet to work out a conversion factor that will convert your moon's orbital semi-major axis from arcseconds to AU; i.e. in the above equation, we will set length = a [AU], 0=a"], and calculate conversion factor ["/AU] = 2πT 360° 1° 3600" × distance. conversion factor = type your answer... "/AU. Note: in order for units to work out, we had to multiply by the number of degrees per arcsecond (") in the above formula.
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![The physical length of the ruler as a fraction of the circumference of the big circle is the same as the angular length of the ruler as a fraction of
360°:
length
circumference
=
0
360°
Since circumference = 2π X radius and the radius of the big circle is the distance to the ruler/planet:
length
=
2π × distance
0
360°
Solving for the physical length of the ruler yields:
Ꮎ
length = 2 × distance x
360°
This general equation can be used along with the distance to your planet to work out a conversion factor that will convert your moon's orbital
semi-major axis from arcseconds to AU; i.e. in the above equation, we will set
length
= a [AU],
0
= a
["],
and calculate
conversion factor ["/AU] :
=
2πT
360°
1°
3600"
× distance.
conversion factor = type your answer...
"/AU.
Note: in order for units to work out, we had to multiply by the number of degrees per arcsecond (") in the above formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3240cc88-1ac6-4d44-9a1b-de7e91360377%2Fd019c19c-cfdb-402a-aa27-7d789ae0ae1f%2F2c9xns_processed.png&w=3840&q=75)
Transcribed Image Text:The physical length of the ruler as a fraction of the circumference of the big circle is the same as the angular length of the ruler as a fraction of
360°:
length
circumference
=
0
360°
Since circumference = 2π X radius and the radius of the big circle is the distance to the ruler/planet:
length
=
2π × distance
0
360°
Solving for the physical length of the ruler yields:
Ꮎ
length = 2 × distance x
360°
This general equation can be used along with the distance to your planet to work out a conversion factor that will convert your moon's orbital
semi-major axis from arcseconds to AU; i.e. in the above equation, we will set
length
= a [AU],
0
= a
["],
and calculate
conversion factor ["/AU] :
=
2πT
360°
1°
3600"
× distance.
conversion factor = type your answer...
"/AU.
Note: in order for units to work out, we had to multiply by the number of degrees per arcsecond (") in the above formula.
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