Please help me to solve this equation. Than you for your time and efforts. Here is the question?
Jupiter at its closest approach to earth is about 630,000,000 kilometers, the diameter of Jupiter is 140,000 km, calculate the angular diameter of Jupiter in arc seconds. 206,265 arcseconds = 1 Radian.
To calculate the angular diameter of Jupiter in arc seconds, we can use the formula:
Angular diameter (in radians) = diameter of Jupiter / distance from Earth to Jupiter
First, we need to convert the diameter of Jupiter from kilometers to meters, since the distance is also given in meters.
Diameter of Jupiter in meters = 140,000 km * 1000 = 140,000,000 meters
Next, we need to convert the distance from kilometers to meters:
Distance from Earth to Jupiter in meters = 630,000,000 km * 1000 = 630,000,000,000 meters
Now, we can substitute these values into the formula to calculate the angular diameter in radians:
Angular diameter (in radians) = 140,000,000 meters / 630,000,000,000 meters ≈ 0.000222 radians
Lastly, to convert radians to arc seconds, we multiply by the conversion factor:
Angular diameter (in arc seconds) = 0.000222 radians * 206,265 arc seconds/radian ≈ 45.8 arc seconds
Therefore, the angular diameter of Jupiter is approximately 45.8 arc seconds.