Take the radius of the earth's orbit to be 1.5 x 1011 m.
a. Using a year to be 365 days, find the speed of the earth as it moves around the sun. __m/s
b. Convert this speed to miles/hour (show your conversion factor in your written backup). __miles/hour
To find the speed of the Earth as it moves around the Sun, we can use the formula:
Speed = Circumference / Time
a. To calculate the speed of the Earth in meters per second (m/s), we need to calculate the circumference of the Earth's orbit. The circumference is equal to 2π times the radius of the orbit.
Circumference = 2π × radius
= 2π × (1.5 x 10^11) m
Next, we need to determine the time it takes for the Earth to complete one orbit around the Sun. Since we're assuming a year to be 365 days, we can convert it to seconds:
Time = 365 days × 24 hours/day × 60 minutes/hour × 60 seconds/minute
Now, we can substitute the values into the formula to calculate the speed in meters per second:
Speed = (2π × (1.5 x 10^11 m)) / (365 days × 24 hours/day × 60 minutes/hour × 60 seconds/minute)
b. To convert the speed from meters per second to miles per hour, we need to multiply the speed by the appropriate conversion factor.
1 mile = 1609.34 meters
1 hour = 3600 seconds
So, the conversion factor is 1609.34 meters/1 mile × 1 hour/3600 seconds.
To convert the speed to miles per hour, we can use:
Speed (in miles/hour) = Speed (in meters/second) × (1609.34 meters/1 mile) × (1 hour/3600 seconds)
By substituting the calculated speed, we can find the speed in miles per hour.
a. To find the speed of the Earth as it moves around the Sun, we can use the equation:
speed = (circumference of Earth's orbit) / (time taken to complete one orbit)
The circumference of a circle can be calculated using the formula:
circumference = 2 * π * radius
Substituting the given radius of the Earth's orbit (1.5 x 10^11 m) into the equation, we get:
circumference = 2 * π * (1.5 x 10^11) m
Since a year is 365 days, the time taken to complete one orbit is 365 days.
However, we need to convert this to seconds since the unit of speed is m/s.
So, time taken in seconds = 365 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute
Substituting the values into the equation, we get:
speed = (2 * π * (1.5 x 10^11) m) / (365 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute)
Calculating this, we get the speed of the Earth around the Sun.
b. To convert the speed from meters per second (m/s) to miles per hour (mph), we can use the following conversion factors:
1 mile = 1609.34 meters
1 hour = 3600 seconds
So, the conversion factor is:
(1 mile/1609.34 meters) * (3600 seconds/1 hour)
Multiply the calculated speed from part a by this conversion factor to get the speed in miles per hour.