You must show your work for full credit.) Calculate the circular speed of an object that orbits the Sun at a distance of 0.2 AU (1 AU = 1.5e+11 meters, the distance between the Earth and the Sun): (Points : 10)
To calculate the circular speed of an object orbiting the Sun, we can use the formula for circular speed, v = 2πr/T, where v is the circular speed, r is the distance between the object and the Sun, and T is the period of the orbit.
First, we need to convert the distance from AU to meters. Given that 1 AU is equal to 1.5e+11 meters, we can multiply the distance of 0.2 AU by 1.5e+11 to get the distance in meters:
Distance = 0.2 AU * 1.5e+11 meters
Distance = 3e+10 meters
Next, we need to find the period of the orbit. The period is the time it takes for the object to complete one full orbit around the Sun. Since the question does not provide the period, we'll need to assume a specific period. For simplicity, let's assume a period of 1 year. The period could be any other value, but this is just for illustrative purposes. Converting 1 year to seconds, we know that 1 year is equal to 365.25 days, and each day has 24 hours, each hour has 60 minutes, and each minute has 60 seconds. Thus, the period in seconds is:
Period = 1 year * 365.25 days * 24 hours * 60 minutes * 60 seconds
Period = 3.1536e+7 seconds
Finally, we can use the formula for circular speed to calculate the value:
v = 2πr/T
v = 2 * π * 3e+10 meters / 3.1536e+7 seconds
v ≈ 1.892e+4 meters per second
Therefore, the circular speed of the object orbiting the Sun at a distance of 0.2 AU is approximately 1.892e+4 meters per second.