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Earth is approximately 93 000 000 mi from the sun. It revolves around the sun, in an almost circular orbit, in about 365 days. Calculate the linear speed, in miles per hour, of Earth in its orbit. Give your answer to the nearest hundredth.

Guest May 12, 2015

Best Answer 

 #1
avatar+26750 
+18

365 days = 365*24 hours

 

Circumferential distance travelled in 365*24 hours = 2*pi*93,000,000 miles

 

Linear speed = distance/time = 2*pi*93,000,000/(365*24) miles per hour

 

$${\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{93\,000\,000}}}{\left({\mathtt{365}}{\mathtt{\,\times\,}}{\mathtt{24}}\right)}} = {\mathtt{66\,705.049\: \!494\: \!029\: \!856\: \!433\: \!1}}$$

 

speed = 66,705.05 miles per hour to nearest hundredth (or did you mean to nearest hundred, in which case speed = 66,700 miles per hour).

.

Alan  May 12, 2015
 #1
avatar+26750 
+18
Best Answer

365 days = 365*24 hours

 

Circumferential distance travelled in 365*24 hours = 2*pi*93,000,000 miles

 

Linear speed = distance/time = 2*pi*93,000,000/(365*24) miles per hour

 

$${\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{93\,000\,000}}}{\left({\mathtt{365}}{\mathtt{\,\times\,}}{\mathtt{24}}\right)}} = {\mathtt{66\,705.049\: \!494\: \!029\: \!856\: \!433\: \!1}}$$

 

speed = 66,705.05 miles per hour to nearest hundredth (or did you mean to nearest hundred, in which case speed = 66,700 miles per hour).

.

Alan  May 12, 2015
 #2
avatar+981 
+15

Assuming that Earth's orbit is circular . . .

Circumference = pi times diameter

Since the sun is the center, the diameter is 2*93000000 = 186000000

C = pi*186000000 = 584336233.5677 miles.

So every 365 days Earth travels 584336233.567701542 miles.

Every 1 day it must travel 584336233.5677/365 =  1600921.187856717 miles.

And every hour 1600921.1878/24 = 66705.049494030 miles.

 

The speed is 66,705.05 miles/hour (nearest hundredth) 

zacismyname  May 12, 2015
 #3
avatar+92781 
+6

WOW.  That is really fast!     

And the cops book us for speeding!!      

Melody  May 12, 2015

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