Calculating earth's speed using radius and speed of light, etc.

In summary, Ole Roemer found that the average delay in the disappearance of Io from one orbit around Jupiter to the next is 14 s. The distance light travels in 14 s is 4.2 x 10^9 m. Earth's speed in km/s is 27.45 km/s, calculated by dividing the distance traveled by Earth in 42.5 h by the time taken. To check the reasonability of this answer, Earth's speed in orbit was calculated using the orbital radius of 1.5 x 10^8 km and the period of one year. However, this calculation was incorrect as it did not take into account Earth's angular velocity and the error between the arc and chord of the angle.
  • #1
DDRchick
27
0
Ole Roemer found that the average increased delay in the disappearance of Io from one orbit around Jupiter to the next is 14 s.
(a) How far does light travel in 14 s?
1 m

(b) Each orbit of Io takes 42.5 h. Earth travels the distance calculated in part (a) in 42.5 h. Find the speed of Earth in km/s.
2 km/s

(c) Check to make sure that your answer for part (b) is reasonable. Calculate Earth's speed in orbit using the orbital radius, 1.5 108 km, and the period, one year.




d=vt
speed of light = 3x10^8




For part (a) i got 4.2e9, which was correct. d=(3x10^8)(14)
For part (b) I got 27.45 km/s which was correct. 4.2e9m = 4.2e6km
Part (c) I don't know...
 
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  • #2
The Earth goes around the sun in a circle. Find the distance around the circle. The time taken to go around, in seconds. Use v = d/t to find the speed.
 
  • #3
Well I figure, radius is half a diameter, right?
So i multiplied the radius (1.5 x 10^8) by two.
then i found the number of seconds in a year, which is 31,536,000.
I even tried just doing (1.5x10^8)/# seconds in a year
and it wa s still wrong.
:(


**Because it won't let me edit the first post...**
orbital radius, 1.5 108 km = 1.5x10^8
 
Last edited:
  • #4
DDRchick said:
Well I figure, radius is half a diameter, right?
So i multiplied the radius (1.5 x 10^8) by two.
then i found the number of seconds in a year, which is 31,536,000.

Isn't the circumference of a circle = 2πr ?
 
  • #5
Light doesn't travel around the circumference of a circle- travels across the diameter.
 
  • #6
I used LowlyPion's equation and plugged in the radius, and then divided by the number of seconds.
It marked it correct. :D
Thanks so much!
 
  • #7
HallsofIvy said:
Light doesn't travel around the circumference of a circle- travels across the diameter.

That may well be, but the question is asking for Earth's speed, and the circumference/period. Earth's speed is relevant for explaining the 14 s interval, and represents an exceedingly small arc of Earth's orbit right?
 
  • #8
hey it is the angular velocity you need to consider i.e omega,not linear velocity
then v=d/t cannot be used .
 
  • #9
Just curious would you have the θ for 14 sec divided by a year load of seconds?

And could you identify the error difference between the arc of θ, and the chord of θ?
 

1. How is the speed of light used to calculate the Earth's speed?

The speed of light is used as a constant in the equation for calculating Earth's speed. This is because the speed of light is the fastest known speed in the universe and provides a reliable benchmark for measuring other speeds.

2. What is the formula for calculating Earth's speed?

The formula for calculating Earth's speed is v = 2πr / T, where v is the Earth's speed, r is the radius of Earth's orbit around the sun, and T is the time it takes for Earth to complete one orbit.

3. How is the radius of Earth's orbit determined?

The radius of Earth's orbit is determined by measuring the distance between Earth and the sun, which is approximately 149.6 million kilometers. This distance is known as an astronomical unit (AU) and is used as the standard unit for measuring distances in the solar system.

4. What is the time it takes for Earth to complete one orbit?

The time it takes for Earth to complete one orbit around the sun is approximately 365.25 days. This number takes into account the leap year, which occurs every four years to keep our calendar in sync with the Earth's orbit.

5. Can this formula be used to calculate the speed of other planets?

Yes, this formula can be used to calculate the speed of any object in orbit around the sun. The only variables that would change are the radius of the orbit and the time it takes for the object to complete one orbit.

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