The earth travels in a nearly circular orbit about the sun. The mean distance of the
earth from the sin is 1.5¡Á1011 m. What is the approximation speed of the earth in
its orbit around the sun?
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You know that it takes 365.25 days for the Earth to make a complete revolution around the sun. So, convert that to seconds and divide it into the circumference of the orbit.
The orbit's circumference is
2 pi*1.5*10^11 m
To find the approximation speed of the Earth in its orbit around the Sun, we can use the relation between the speed, distance, and time.
1. The mean distance of the Earth from the Sun is given as 1.5 × 10^11 m.
2. The Earth completes one orbit around the Sun in approximately 365.25 days.
3. To calculate the speed of the Earth, we need to convert the time to seconds. There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute.
Therefore, the total number of seconds in a year is: 365.25 days × 24 hours × 60 minutes × 60 seconds ≈ 3.15576 × 10^7 seconds.
4. Now, we can calculate the approximate speed of the Earth using the formula: speed = distance / time.
speed ≈ (1.5 × 10^11 m) / (3.15576 × 10^7 s).
5. Simplifying the calculation gives us: speed ≈ 4.74 × 10^3 m/s.
Therefore, the approximation speed of the Earth in its orbit around the Sun is approximately 4.74 × 10^3 m/s.
To calculate the approximation speed of the Earth in its orbit around the Sun, we can make use of Kepler's Third Law of planetary motion. According to this law, the square of a planet's orbital period (T) is proportional to the cube of its mean distance from the Sun (r):
T^2 = k * r^3
Where T is measured in years, r is measured in Astronomical Units (AU), and k is a constant.
The mean distance of the Earth from the Sun is given as 1.5 * 10^11 m. To convert this distance to AU, we need to divide it by the average distance from the Earth to the Sun, which is approximately 1 AU (149.6 million km or 93 million miles).
So, the Earth's mean distance from the Sun in AU is:
r = (1.5 * 10^11 m) / (1 AU)
Now, we need to find the orbital period of the Earth. The Earth orbits around the Sun once in approximately 365.25 days (1 year).
Plugging these values into Kepler's Third Law equation, we can solve for T:
T^2 = k * r^3
(365.25)^2 = k * (r)^3
Simplifying further, we can solve for k:
k = (365.25)^2 / (r)^3
Now that we have the value of k, we can calculate the approximation speed of the Earth in its orbit around the Sun. The speed of the Earth is given by the formula:
Speed = Circumference / Time period
The circumference of the Earth's orbit can be approximated as the circumference of a circle with a radius equal to the Earth's mean distance from the Sun (r).
Circumference = 2 * π * r
Substituting the value of r and the calculated value of k into the equation, we can solve for the speed of the Earth:
Speed = (2 * π * r) / T
Calculating these values will provide the approximation speed of the Earth in its orbit around the Sun.