Distance in space cannot be measured directly. They must be calculated based upo
ID: 3162591 • Letter: D
Question
Distance in space cannot be measured directly. They must be calculated based upon measurements that can be made from Earth, such as angles and illumination. Use Wolfram I Alpha to fill in the following table of data. You may have to search each planet separately. Round values to 2 decimal places. Use the Wolfram I Alpha search for "Astronomical Unit" to determine the value, in miles, for 1 AU: Do you see any pattern, either linear or quadratic, between distance and light travel time? Find a formula that represents the linear relationship between a planet's distance from the Sun and a planet's light Travel Time from the sun.Explanation / Answer
2. using data from Wolfram|alpha : 1 milllion miles=.01076AU
b) To get light travel time we divide total distance by the speed of light. Now the distance is considered in vaccum so if x is the distance and c is the speed of light then total time t=x/c and c in vaccum=3*10^8 m/s
Lets consider the example of mars then its distance from sun= 1.47AU= 1.47*1.5*10^11m
then total time =1.47*1.5*10^11m/3*10^8m/s=.735*10^3sec= 12.25min
from the given table the first difference: .26, .27 ,.48 ,3.99 ,4.59 ,9.89 .10.01(distance difference in AU)
and the second difference: .01, .21, 3.51, .6, 5.3, .12
the pattern shows that x and t has a quadtratic relationship where c is constant=3*10^8m/s
4. if we consider light speed as constant then the linear relationship between distance and travel time is like
d=u*t where d is the distance and u is the light velocity, t is the light travel time if u=c=constant then we can write d=u
Planet Distance from sun(AU) Distance from Sun(miles) Mercury .43 40.32million Venus .72 66.79million Earth .99 98.99million Mars 1.47 136.30million Jupiter 5.46 507.20million Saturn 10.05 934.40million Uranus 19.94 1.85billion Neptune 29.95 2.78billion