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?
To calculate the average speed of Earth in its orbit, we need to know the time it takes for Earth to complete one full revolution around the Sun. This is usually referred to as the orbital period.
a) Calculate the average speed of Earth in its orbit (assumed to be circular) in meters per second:
The average speed is defined as the total distance traveled divided by the total time taken.
Given:
- Average distance between Earth and the Sun = 1.5 ✕ 10^11 m
To find the orbital period, we need to know the time it takes for Earth to complete one revolution around the Sun.
The orbital period for Earth is approximately 365.25 days, which is the time it takes for Earth to complete one orbit around the Sun. We can convert this to seconds by multiplying by 24 hours (in a day), 60 minutes (in an hour), and 60 seconds (in a minute):
365.25 days × 24 hours/day × 60 minutes/hour × 60 seconds/minute
Now that we have the orbital period, we can calculate the average speed:
Average speed = Total distance traveled / Total time taken
= 2πr / T
where:
- r is the average distance between Earth and the Sun
- T is the orbital period of Earth
Calculating the average speed:
Average speed = (2π * 1.5 ✕ 10^11 m) / (365.25 days × 24 hours/day × 60 minutes/hour × 60 seconds/minute)
Simplifying the expression, we get:
Average speed ≈ (2 * 3.14159 * 1.5 ✕ 10^11 m) / (31557600 s)
Evaluating this calculation will give us the average speed of Earth in its orbit in meters per second.
b) To convert the average speed from meters per second to miles per hour, we need to know the conversion factor between the two. The conversion factor is 1 meter per second = 2.23694 miles per hour.
To convert the average speed from meters per second to miles per hour, we can multiply the average speed (in meters per second) by the conversion factor:
Average speed (mph) = Average speed (m/s) × 2.23694
By performing this calculation, we will obtain the average speed of Earth in its orbit in miles per hour.
a) To calculate the average speed of Earth in its orbit, we can use the formula:
Average speed = distance / time
The distance between Earth and the Sun is given as 1.5 ✕ 10^11 m.
The time it takes for Earth to complete one orbit around the Sun is approximately 365.25 days (including the extra leap year day every 4 years).
We need to convert this time to seconds in order to use the same units for distance and time. There are 24 hours in a day and 60 minutes in an hour, so we multiply 365.25 days by 24 hours, then by 60 minutes, and finally by 60 seconds:
Time = 365.25 days × 24 hours × 60 minutes × 60 seconds = 3.15576 ✕ 10^7 seconds (approx.)
Now we can calculate the average speed:
Average speed = 1.5 ✕ 10^11 m / 3.15576 ✕ 10^7 s ≈ 4.75 ✕ 10^3 m/s
Therefore, the average speed of Earth in its orbit is approximately 4.75 ✕ 10^3 m/s.
b) To convert the average speed from meters per second to miles per hour, we can use conversion factors:
1 mile = 1609.34 meters
1 hour = 3600 seconds
So, we can convert the units as follows:
Average speed in miles per hour = (4.75 ✕ 10^3 m/s) × (1 mile / 1609.34 meters) × (3600 seconds / 1 hour)
After performing the calculations, we find:
Average speed ≈ 1.677 ✕ 10^4 miles per hour
Therefore, the average speed of Earth in its orbit is approximately 1.677 ✕ 10^4 miles per hour.
distance traveled=2PI(1.5e11)
time=365days(24hr/day)(3600sec/nr)=3.15e7
speed= 2PI*1.5e11/3.5e7= 26.9e3m/sec