Period and duration of Earth-Mars Hohmann transfer orbit

[HoboMoo]

I just don't even know where to begin. I'm not sure what formulas to use and just can't do anyhting with it. any help would be great. Thanks!

Recall that your trip to Mars is accomplished by using an elliptic transfer orbit going from Earth to Mars as shown in Fig. 1. This trajectory assumes that Earth at departure, the Sun, and Mars at arrival, are aligned. You calculated that the semi-major axis for this transfer orbit was a= 190100208000 m.

How long, in days, would the interplanetary trip last? Hint: first, determine the period of the transfer orbit.

 

[DrStupid]

How about Kepler's third law?

 

[HoboMoo]

So if a=190100208000m, its P^2=19010020800^3?

If that's the case, i get P^2= 6.8699 E 33 and square root that to get P?

P=8.2885 E 16?

 

[gneill]

Kepler's third law (in its original form) is a law of proportionality, not equality. To make it an equality you would have to use either a suitable (i.e. special) choice of units, a constant of proportionality, or form a ratio with another known pair of semi-major axis and period. So:

$$P^2 \propto T^3 $$
$$P^2 = k\;T^3$$
$$\frac{P2^2}{P1^2} = \frac{T2^3}{T1^3}$$
The last version is probably the easier to use if you happen to know of another suitable body orbiting the Sun for which you know the semi-major axis and the orbital period