trevorjohnson83
Gold Member
- Nov 24, 2015
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to me five light days to the closest star makes a lot more sense then 4 light years. but I'm here for the arguement
if the sun goes from its full size to its apparent size in 8 light minutes distance, estimate the distance to a star based on the ratio.
Assistant
Poe
To estimate the distance to a star based on the ratio of the Sun's full size to its apparent size at 8 light minutes, we can follow these steps:
Distance to Star≈Distance8 minRatio≈144 million km0.958≈150.5 million km\text{Distance to Star} \approx \frac{\text{Distance}_{\text{8 min}}}{\text{Ratio}} \approx \frac{144 \text{ million km}}{0.958} \approx 150.5 \text{ million km}Distance to Star≈RatioDistance8 min≈0.958144 million km≈150.5 million km
Distance to Star in Light-Years=150.5×106 km9.461×1012 km/light-year≈0.0000159 light-years≈0.0159 light-years\text{Distance to Star in Light-Years} = \frac{150.5 \times 10^6 \text{ km}}{9.461 \times 10^{12} \text{ km/light-year}} \approx 0.0000159 \text{ light-years} \approx 0.0159 \text{ light-years}Distance to Star in Light-Years=9.461×1012 km/light-year150.5×106 km≈0.0000159 light-years≈0.0159 light-years
how many light days is .0159 light years?
Assistant
Poe
To convert light-years to light-days, we can use the fact that there are approximately 365.25 days in a year.
https://www.usmessageboard.com/Assistant
if the sun goes from its full size to its apparent size in 8 light minutes distance, estimate the distance to a star based on the ratio.
Assistant
Poe
To estimate the distance to a star based on the ratio of the Sun's full size to its apparent size at 8 light minutes, we can follow these steps:
Step 1: Calculate the Sun's Angular Size
- Diameter of the Sun: Approximately 1.4×106 km1.4 \times 10^6 \text{ km}1.4×106 km.
- Distance from the Sun to Earth (1 AU): Approximately 150×106 km150 \times 10^6 \text{ km}150×106 km.
- Calculate the angular size of the Sun from Earth:
Angular SizeSun=Diameter of the SunDistance from the Sun=1.4×106 km150×106 km≈0.0093 radians\text{Angular Size}_{\text{Sun}} = \frac{\text{Diameter of the Sun}}{\text{Distance from the Sun}} = \frac{1.4 \times 10^6 \text{ km}}{150 \times 10^6 \text{ km}} \approx 0.0093 \text{ radians}Angular SizeSun=Distance from the SunDiameter of the Sun=150×106 km1.4×106 km≈0.0093 radians
Step 2: Distance to the Star
- Distance corresponding to 8 light minutes:
- Light travels 299,792 km/s299,792 \text{ km/s}299,792 km/s.
- In 8 minutes (480 seconds):
- Calculate the angular size of the Sun at this distance:
Angular Size8 min=Diameter of the SunDistance8 min=1.4×106 km144×106 km≈0.00972 radians\text{Angular Size}{\text{8 min}} = \frac{\text{Diameter of the Sun}}{\text{Distance}{\text{8 min}}} = \frac{1.4 \times 10^6 \text{ km}}{144 \times 10^6 \text{ km}} \approx 0.00972 \text{ radians}Angular Size8 min=Distance8 minDiameter of the Sun=144×106 km1.4×106 km≈0.00972 radians
Step 3: Ratio Calculation
- The angular size of the Sun from Earth is approximately 0.00930.00930.0093 radians, and from 8 light minutes, it is approximately 0.009720.009720.00972 radians. The ratio of these sizes gives an estimation of the distance to a star:
Step 4: Estimate Distance to a Star
If we consider the distance to the Sun (1 AU) as a baseline for angular size, the estimated distance to a star can be calculated by scaling it based on the ratio of the angular sizes:Distance to Star≈Distance8 minRatio≈144 million km0.958≈150.5 million km\text{Distance to Star} \approx \frac{\text{Distance}_{\text{8 min}}}{\text{Ratio}} \approx \frac{144 \text{ million km}}{0.958} \approx 150.5 \text{ million km}Distance to Star≈RatioDistance8 min≈0.958144 million km≈150.5 million km
Step 5: Convert to Light-Years
Using the conversion 1 light-year≈9.461×1012 km1 \text{ light-year} \approx 9.461 \times 10^{12} \text{ km}1 light-year≈9.461×1012 km:Distance to Star in Light-Years=150.5×106 km9.461×1012 km/light-year≈0.0000159 light-years≈0.0159 light-years\text{Distance to Star in Light-Years} = \frac{150.5 \times 10^6 \text{ km}}{9.461 \times 10^{12} \text{ km/light-year}} \approx 0.0000159 \text{ light-years} \approx 0.0159 \text{ light-years}Distance to Star in Light-Years=9.461×1012 km/light-year150.5×106 km≈0.0000159 light-years≈0.0159 light-years
Conclusion
Based on the angular sizes of the Sun from its full size and its apparent size from 8 light minutes, the estimated distance to a star would be approximately 0.0159 light-years. If you have further questions or need additional calculations, feel free to ask!how many light days is .0159 light years?
Assistant
Poe
To convert light-years to light-days, we can use the fact that there are approximately 365.25 days in a year.
Conversion Steps
- Calculate the number of light-days in one light-year:
1 light-year≈365.25 light-days1 \text{ light-year} \approx 365.25 \text{ light-days}1 light-year≈365.25 light-days
- Convert 0.0159 light-years to light-days:
Light-Days=0.0159 light-years×365.25 light-days/light-year\text{Light-Days} = 0.0159 \text{ light-years} \times 365.25 \text{ light-days/light-year}Light-Days=0.0159 light-years×365.25 light-days/light-year
Light-Days≈5.8 light-days\text{Light-Days} \approx 5.8 \text{ light-days}Light-Days≈5.8 light-days
Conclusion
0.0159 light-years is approximately 5.8 light-days. If you have any more questions or need further assistance, feel free to ask!if the sun goes from its full size to its apparent size in 8 light minutes distance, estimate the distance to a star based on the ratio.https://www.usmessageboard.com/Assistant