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

[DDRchick]

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...

 

[Delphi51]

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.

 

[DDRchick]

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

 

[LowlyPion]

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 ?

 

[HallsofIvy]

Light doesn't travel around the circumference of a circle- travels across the diameter.

 

[DDRchick]

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!

 

[LowlyPion]

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?

 

[monty37]

hey it is the angular velocity you need to consider i.e omega,not linear velocity
then v=d/t cannot be used .

 

[LowlyPion]

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?