Earth is about 150,000,000 km from the Sun. How long did it take light to cross Earth's orbit in Rømer's experimental determination of the speed of light?
A)about 8 seconds
B)about 16 seconds
C)about 8 minutes
D)about 16 minutes

Question

Quizplus · Accepted Answer

The time taken by light to cross Earth's orbit in Rømer's experiment can be calculated by using the equation:
Speed of light = distance/time
Given: distance = 150,000,000 km
We need to find the time taken, which can be rewritten as:
time = distance/speed of light
In Rømer's experiment, the speed of light was not known, but the time difference between two eclipses of Jupiter's moon, Io, was measured. This time difference was due to the varying distance between Earth and Jupiter as they revolve around the Sun. When Earth is closer to Jupiter, the time difference is shorter, and when Earth is farther away, the time difference is longer.

Rømer found that the time difference was about 11 minutes when Earth was on one side of the Sun and about 16 minutes when Earth was on the opposite side of the Sun. This means that it took light 5 minutes longer to cross Earth's orbit when Earth was on the opposite side of the Sun compared to when it was on the same side.

Therefore, when Earth is on the same side of the Sun as Jupiter, the time taken for light to cross Earth's orbit would be:
time = distance/speed of light = 150,000,000 km / speed of light

When Earth is on the opposite side of the Sun, the time taken for light to cross Earth's orbit would be:
time = (150,000,000 km + diameter of Earth's orbit) / speed of light

The diameter of Earth's orbit is about 2 times the radius of Earth's orbit, which is about 300,000 km. Therefore, the time taken for light to cross Earth's orbit on the opposite side of the Sun would be:
time = (150,000,000 km + 600,000 km) / speed of light
= 150.6 million km / speed of light

From Rømer's measurements, we know that the time difference between the two scenarios is 5 minutes. Therefore:
16 minutes - 11 minutes = 5 minutes

This means that it took light 5 minutes longer to travel the extra distance (600,000 km) when Earth was on the opposite side of the Sun.

Using these equations, we can solve for the speed of light:
150,000,000 km / speed of light - (150,600,000 km / speed of light) = 5 minutes

Simplifying, we get:
(150,000,000 km - 150,600,000 km) / speed of light = 5*60 seconds

Solving for the speed of light, we get:
speed of light = (600,000 km)/(300 seconds)
= 2000 km/s

Finally, we can use the distance of Earth's orbit and the speed of light to calculate the time taken for light to cross Earth's orbit:
time = 300,000 km / 2000 km/s
= 150 seconds or approximately 2.5 minutes

Therefore, the answer is:
D) about 16 minutes

Earth Is About 150,000,000 Km from the Sun