Escape velocity when in earth's orbit

[University]

I have a problem where it ask to find the period/time(using Kepler's 3rd law) of an unpowered spacecraft to move from Earth's orbit to Mars orbit using the transfer orbit approach.

I found P/T using kepler's 3rd law but the second part ask to find how fast the spacecraft need to be moving at the beginning of its trip i.e while in Earth's orbit using

V²= GM(2/r-1/a) where a is the semi-major axis of the orbit, r distance from the sun.

Now the units of a is in astronomical units and r can also be AU, what units would V^2 be if I use AU for both r and a in the Vis Viva equation above?

 

[russ_watters]

Is G also in units of AU?

 

[University]

Is a velocity of 3.27 * 10⁴ m/s seems correct for an escape velocity of a unpowered spacecraft that use the least energy transfer orbit to escape the Earth's orbit and head to Mar's orbit?

 

[qraal]

If you set r & a equal to AU, and G & M equal to 1, the the units are Earth's average orbital speed, thus v^2=1. Actually slightly different to its real speed because we're ignoring Earth's mass, but that's a refinement for more advanced computations.

 

[Radrook]

Can someone please translate that into miles per second?

 

[University]

try google

 

[qraal]

Can someone please translate that into miles per second?

Earth's orbital speed is 18.5 mi/s on average.