What is the angular speed in rev/min of the Earth as it orbits around the sun?
I'm confused with this problem. I know we have to convert from rad/s to rev/rad to s/min in order to get the units as rev/min. But I don't know what to use for rad/s
Thye following is more than you asked for but I hope you find it interesting.
I think you would be surprised to know just how many people have no idea that the Earth moves at all, thinking that the Sun revolves around the Earth. The motion of our Earth through space is really very complex. It rotates, or spins, on its axis; it moves in a near circular path, or revolves, around our Sun; it wobbles about its center; and it sinuates and nods. All the time it is undergoing these spacial motions, its internal masses are swirling, heaving, and drifting. Lets start at the beginning. Lets explore.
Our Earth is an approximately spherical body, actually an oblate spheroid of ~3963 miles equatorial radius and ~3950 miles polar radius, (Astronomical Almanac-1997, pg. E88) rotating 360 degrees on its axis, once in 23 hours- 56 minutes 04.091 seconds, the sidereal day. The 24 hour clock day that we experience daily, the mean solar day, or the synodic day, is the period of time that it takes for the same point on the earth's surface to cross the line joining the earth and the sun. The axis of rotation passes through the center of the earth and pierces its surface at the north and south poles. The rotation of the earth on its axis from west to east in a period of one day makes all celestial bodies, sun, moon, planets and stars, appear to turn around the earth from east to west, in the same period. Therefore the rotation of the earth is counterclockwise, looking down at the north pole. As you stand on the equator, you are actually moving at a rotational speed of ~1038 MPH relative to the Earth's axis.
Our earth also completes one 360 degree revolution, or orbit, around the Sun in a period of ~365-1/4 days, or what we call, a year. The orbit of the Earth is elliptical in shape with the closest distance from the Sun being ~91,408,000 miles and the farthest distance being ~94,513,000 miles. The mean distance of the Earth from the Sun is often quoted as being 93,000,000 miles. The earth's axis is tilted to its orbital plane at an angle of ~23 1/2 degrees. The revolution of the earth in its orbit around the Sun makes the Sun appear to shift gradually eastward among the stars in the course of the year. Therefore the revolution of the Earth around the Sun is also counterclockwise, as viewed from above the Earth's north pole.The apparant path of the Sun among the stars is called the ecliptic. The eastward motion of the Earth in its orbit, along the ecliptic, is approximately 1 degree per day. The mean translational speed of the earth in its orbit is ~66,660 MPH.
Our solar system, as a whole, is within the Milky Way Galaxy, the Sun being ~30,000 light years (one light year is the distance light travels in one year, ~5.89x10^12 miles) from the center of the galaxy and, with its family of planets, rotating about the center of the galaxy at a speed of ~563,000 mph.. Even at this tremendous speed, our solar system requires about 200-220 million years to complete one revolution within the galaxy. Our whole galaxy appears to be hurtling through space at a speed of over one million miles per hour. Hold on to your hat!
Amazing isn't it? Just think, at any instant of time, you, standing on the equator on the side of the Earth away from the Sun, are moving through the emptiness of space at a combined speed of 1038 + 66,600 + 563,000 + 1,000,000 = ~1,630,628 MPH. What a breeze !
As complex as all of that might seem, in reality there are several other smaller, less obvious, perturbations of the Earth's motion that affect your motion and are intertwined with the major spacial motion. The actual orbit of the Earth around the Sun is not a smooth elliptical path as we might suspect. In actuality, the combined Earth-Moon system, or the center of mass of the two bodies, is what traverses the truly elliptical path around the Sun. In doing so, the Earth actually moves in a sinusoidal path about the mean elliptical path, moving ~1500 miles outside of, and inside of, the mean elliptical path of the combined mass center like a roller coaster.
The Earth's axis goes through several amazing gyrations also. It gyrates counterclockwise approximately 6 inches a day around the geographic north pole in what is referred to as the Chandler wobble. The motion has two components, one annual and the other over a 14 month period. The annual component is apparently associated with the the planets seasonal conditions. The other, called the Chandler component, is apparently a free oscillataion of unknown origin. When the two components are out of phase, they tend to cancel each other. However, when they are in phase with one another, the path of the axis wanders by as much as 6 inches per day. The in phase cycle repeats itself approximately every 6 years.
On top of the wobbling, the axis nods back and forth as if in a bowing motion due to the Earth's gravitational interaction with the Moon. I take approximately 18.6 years for the axis to complete a nod of ~9.2 seconds of arc.
At the same time, the polar axis is rotating counterclockwise, or precessing, about a line perpendicular to the ecliptic plane. The axis takes ~25,800 years to complete one revolution with the effect of precessing the equinoxes westward (retrograde) which is why the period of time between the Vernal Equinoxes (365.2422 days) is shorter than the time period for the Earth to complete a 360 degree revolution about the Sun (365.2564 days) relative to the stars. Another effect of this precession is the changing of the North Star, currently Polaris. Polaris is really about 70 minutes away from the true north polar axis and moving closer by about 17 seconds each year. It will be closest to Polaris, around 25 minutes, in the year 2105. Around 13,000 A.D., the star Vega will be the brightest pole star.
The angle of the Earth's axis to the ecliptic also varies between 21deg-39min and 24deg-36 min at the rate of ~.013 degrees per century, taking ~41,000 years to complete a cycle.
Another startling variation in our motion is the change in the average distance between the Earth and Sun due to the constant changing of the orbit's shape between elliptical and circular. This cycle takes ~ 93,000 years to complete and brings the earth about 3 million miles closer to, or farther away from, the Sun than the nominal distance.
To find the angular speed of the Earth as it orbits around the sun in rev/min, you will need to follow a series of unit conversions.
First, you need to understand that angular speed is measured in radians per second (rad/s). It represents the rate at which an object rotates or moves in a circular path.
The Earth completes one full orbit around the sun in approximately 365.25 days. To convert this into seconds, you need to multiply by the number of seconds in a minute (60 seconds) and the number of minutes in an hour (60 minutes). This can be calculated as follows:
365.25 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 31,557,600 seconds.
Now, divide the Earth's total angle traveled in one revolution around the sun (which is 2π radians) by the time it takes to complete the orbit (31,557,600 seconds). This will give you the angular speed in radians per second:
Angular speed = 2π radians / 31,557,600 seconds.
To convert the angular speed from rad/s to rev/min, you'll need to perform one more set of unit conversions.
1 revolution (rev) is equivalent to 2π radians (one full circle), and 1 minute is equal to 60 seconds. Therefore, the conversion factor is:
1 revolution / 2π radians * 60 seconds / 1 minute.
Multiply this conversion factor by the original angular speed in rad/s:
Angular speed in rev/min = (Angular speed in rad/s) * (1 revolution / 2π radians) * (60 seconds / 1 minute).
After substituting the angular speed in rad/s calculated earlier, you can solve the equation to find the angular speed in rev/min of the Earth as it orbits around the sun.