Hubble Law Example using relative vr and relative d

Car �B� is the Highway Patrol � using a radar gun which can find speed and distance to other cars � but can�t see the ground.

Car

d

vr

t0 = 1/H0

d� relative to B

vr �relative to B

t0 = 1/H0

A

�30 miles

15 miles/hr

2 hr

-70 miles

-35miles/hr

2 hr

B

100 miles

50 miles/hr

2 hr

�� 0 miles

�� 0 miles/hr

�----

C

120 miles

60 miles/hr

2 hr

�20 miles

�10 miles/hr

2 hr

D

140 miles

70 miles/hr

2 hr

�40 miles

�20 miles/hr

2 hr

You get the same result whether you use �absolute� velocities and distances, or measure velocities relative to any arbitrary car. Every driver thinks they are at the center of the �car universe� and the other cars are just heading away from them, all having left at some common start time.