Question

In 2006, the asteroid 7934 Sinatra made its closest approach to Earth at 2.24×10^−5 light years away. How far is the distance in miles? (1 light year = 9.46×10^15 meters)

a) 2.12 million miles
b) 2.38 million miles
c) 2.66 million miles
d) 3.01 million miles

Answer 1

After converting from light years to meters and then from meters to miles, asteroid 7934 Sinatra was approximately 2.12 million miles away from Earth in 2006 making option (a) the correct distance.

Step-by-step explanation:

To calculate the distance in miles that the asteroid 7934 Sinatra was from Earth in 2006 when it made its closest approach, we first need to convert the distance from light years to meters, and then from meters to miles. Using the given information, 1 light year is equal to 9.46×1015 meters. Thus, the distance in meters is 2.24×10-5 light years × 9.46×1015 meters/light year.

Now, to convert light years to miles, we use the fact that 1 mile is approximately 1609.34 meters. Therefore, we need to divide the distance in meters by 1609.34 to find the distance in miles. After performing the necessary calculations, we find that the distance is approximately 2.12 million miles, which makes option (a) the correct choice.