The Mars Odyssey spacecraft was launched on April 7, 2001. It underwent orbital insertion. To minimize the amount of fuel required for the insertion process, a highly elliptical orbit was chosen, but circular orbits are far superior for the type of mapping work in which the Mars Odyssey will engage. The elliptical insertion orbit was therefore slowly circularized using an Aerobreaking maneuver that lasted several yrs. Currently, the Mars Odyssey is collecting data at an average orbital altitude of 419.5 km and an orbital period of 1.964 hours. From these data alone, plus the raduis of Mars (3395 km), determine the mass of Mars.
E= .5mv^2 - (GMm)/r
The Attempt at a Solution
I found the velocity of the spacecraft by dividing the circumference of the orbit by the time and got 12203.2 km/hr
Now i used the equation above. Both m's cancel and i solved for M. I got a value of 4.26e21.
Now the actual mass of mars is 6.42e23.
Any help is appreciated! Thanks!