Question

In August 2011, the Juno spacecraft was launched from Earth with the mission of orbiting Jupiter in 2016. The closest distance between Jupiter and Earth is 391 million miles. (a) If it takes 5.0 years for Juno to reach Jupiter, what is its average speed in mi/hr over this period? (b) Once Juno reaches Jupiter, what is the minimum amount of time it takes for the transmitted signals to travel from the spacecraft to Earth?

Answer 1

(a) 8927 mi/h

In order to calculate the average speed, we need to convert the time (t=5.0 y) into hours first. In 1 year, we have 365 days, each day consisting of 24 hours, so the time taken is:

$t=(5.0 y)(365 d/y)(24 h/d)=43,800 h$

The distance covered by the spacecraft is

$d=391 mil. mi = 391\cdot 10^6 mi$

Therefore, the average speed is just the ratio between the distance covered and the time taken:

$v=\frac{d}{t}=\frac{391\cdot 10^6 mi}{43,800 h}=8,927 mi/h$

(b) 35 minutes (2097 seconds)

The transmitted signals (which is a radio wave, which is an electromagnetic wave) travels back to the Earth at the speed of light:

$c=3.0\cdot 10^8 m/s$

Since 1 miles = 1609 metres, the distance covered  by the signal is

$d=391\cdot 10^6 mi \cdot (1609 m/mi)=6.29\cdot 10^{11} m$

So, the time taken by the signal will be

$t=\frac{d}{v}=\frac{6.29\cdot 10^{11} m}{3.0\cdot 10^8 m/s}=2097 s$

And since 1 minute = 60 sec, the time taken is

$t=2097 s \cdot \frac{1}{60 s/min}\sim 35 min$