The planet pluto travels once around the sun every 248 years at a mena distance from the sun of 5890x10^6 km. Find its orbital speed around the sun in (m/s).
The distance around the Sun must be 2PI*radius. Change that to meters.
The time to go around is 248 years. Change that to seconds.
speed= distance/time
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2*PI*5890E6 km/248years in m/s
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To find the orbital speed of Pluto around the Sun, we can use the formula:
Orbital speed = 2 * π * Mean distance from the Sun / Orbital period
Given:
Mean distance from the Sun, R = 5890x10^6 km
Orbital period, T = 248 years
First, we need to convert the mean distance from the Sun to meters, as the final answer should be in meters per second.
1 km = 1000 meters
Therefore, the mean distance from the Sun, R = 5890x10^6 km * 1000 = 5.89x10^9 meters
Next, we need to convert the orbital period from years to seconds.
1 year = 365.25 days (taking into account the leap year)
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
Orbital Period in seconds = 248 years * 365.25 days * 24 hours * 60 minutes * 60 seconds
Orbital Period in seconds = 7.82x10^9 seconds
Now, we can substitute the values into the formula to calculate the orbital speed:
Orbital speed = 2 * π * Mean distance from the Sun / Orbital period
Orbital speed = 2 * π * 5.89x10^9 meters / 7.82x10^9 seconds
Calculating this expression will provide us with the answer in meters per second:
Orbital speed = 2 * 3.14159 * 5.89x10^9 / 7.82x10^9
Orbital speed = 18.66 km/s
Therefore, the orbital speed of Pluto around the Sun is approximately 18.66 km/s.