On January 22,2003 the distance between Sun and Pioneer 10 was 21,275,527,680,000m=2.12*10^13m

now on january 2009 the pioneer 10 has alreay covered 6 yrs of time

so , 6yrs= 1.892*10^8sec

and S=V.t

the relative velocity V=12.24Km/s and t=1.892*10^8sec

then in 6 years the pioneer 10 has covered distance d=12.24*1.892*10^8Km=23.1508080*10^8km=231508080000m

so overall distance=21275527680000m + 2315080800000m=.**2150*10^14m**

Aldebaran was in the distance 6.15*10^7m

then in 6 years=1.892*10^8sec the distance will be 6.15*10^7*1.892*10^8m=1.16358*10^16m

in 2009 the distance between aldebaran and pioneer 10 is=1.16358*10^16-.2150*10^14m=1.1614*10^16m

the speed of pioneer= 12.24km/s=12240m/s

so pioneer covers 12240m in one sec

pioneer covers 1m in 1/12240sec

then pioneer covers 1.1614*10^16m in 1.1614*10^16*1/12240sec=.0000947*10^16sec=3.029*10^-12yr

jjennylove Sep 26, 2019

#1**+1 **

For your answers, all of your steps seem correct!

Does your teacher check for the exact answer? If you are a hundredth of a thousandth off, does your teacher consider it wrong?

Your answers and solution steps seem accurate, so you should be fine.

You can see what other people say though.

CalculatorUser Sep 26, 2019

#2**+2 **

Here is how long it should take Pioneer 10 spacesraft to reach the star Aldebaran. According to Wikipedia, the distance to Aldebaran is ~65.3 light years from the Sun.

The speed of light is: 299,792.458 km/second.

The speed of Pioneer 10 is 12.24 km/second.

299,792.458 / 12.24 =24,492.85 times is the speed of light faster than the speed of the spacecraft.

Therefore, it will take Pioneer 10:

**24,492.85 x 65.3 =1,599,383 Earth years to reach Aldebaran. Make sure that your final answer agrees roughly with this number.**

Guest Sep 27, 2019

edited by
Guest
Sep 27, 2019