The average distance between Earth and the Sun is 1.5 ✕ 10^11 m.
(a)Calculate the average speed of Earth in its orbit (assumed to be circular) in meters per second.
(b)What is this speed in miles per hour?
what is the length of the orbit? (circumference of the circle)
what is the time of the orbital period? (year)
... convert to seconds and divide into the orbit length to find speed
convert m/s to mph ... google will do this conversion
Well, I suppose it does about 2 pi R in 365 days
for m/s:
v = 2 pi R/T = 2 pi *1.5*10^11 m / (365 d*24h/d*3600s/h)
now for part b convert m/s to mi/h
To calculate the average speed of Earth in its orbit, we need to use the formula:
v = 2πr / T
Where:
v = average speed of Earth in its orbit
r = average distance between Earth and the Sun
T = period of Earth's orbit
Given that the average distance between Earth and the Sun is 1.5 ✕ 10^11 m, we can use this value for r. The period of Earth's orbit is approximately 365 days.
(a) Calculate the average speed of Earth in its orbit in meters per second:
v = 2π (1.5 ✕ 10^11 m) / (365 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute)
First, we need to convert the period from days to seconds:
365 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 31,536,000 seconds
Now, we can calculate the average speed:
v = 2π (1.5 ✕ 10^11 m) / 31,536,000 seconds
v ≈ 29,819.7 m/s
Therefore, the average speed of Earth in its orbit is approximately 29,819.7 meters per second.
(b) To convert this speed to miles per hour, we need to use the conversion factor:
1 mile ≈ 1609.34 meters
1 hour ≈ 3600 seconds
So, to convert the speed from meters per second to miles per hour, we can multiply the speed by the conversion factor:
v = (29,819.7 m/s) * (1 mile/1609.34 m) * (3600 seconds/hour)
v ≈ 66,607.7 miles/hour
Therefore, the average speed of Earth in its orbit is approximately 66,607.7 miles per hour.
To calculate the average speed of Earth in its orbit, we need to use the formula for speed:
Speed = Distance / Time
(a) To find the average speed in meters per second, we need to know the time it takes for Earth to complete one orbit around the Sun. The time taken for one complete orbit is approximately 365.25 days, or 31,557,600 seconds.
Therefore, the average speed of Earth in its orbit can be calculated as:
Speed = (1.5 ✕ 10^11 m) / (31,557,600 s)
Speed ≈ 4740.81 m/s
So, the average speed of Earth in its orbit is approximately 4740.81 meters per second.
(b) To convert this speed into miles per hour, we need to use the conversion factor:
1 mile = 1609.34 meters
1 hour = 3600 seconds
So, the conversion factor is:
(1 mile) / (1609.34 meters) × (3600 seconds) / (1 hour)
Now we can calculate the speed in miles per hour:
Speed = (4740.81 m/s) × (1 mile / 1609.34 meters) × (3600 seconds / 1 hour)
Speed ≈ 10,621.65 miles per hour
Therefore, the average speed of Earth in its orbit is approximately 10,621.65 miles per hour.