How Is the Mass of Mars Calculated Using Orbital Data?

[iamkristing]

Homework Statement

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.

Homework Equations

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!

 

[dynamicsolo]

If you used the value for G as 6.67 x 10^-11 , that is in SI metric units, which are kilograms, meters and seconds, did you convert your distances from kilometers to meters? Did you convert your velocity from km/hr to m/sec? When you used the radius of the orbit, did you use the radius of Mars plus the average altitude?

As a tip, when asking for help with a calculation here, it is a good idea to show your work, rather than just asking about your results. It is pretty difficult to see where you may have made an error if we can't see what you were doing...

 

[iamkristing]

Thanks I did mess up on the units. And ill make sure to write it out next time!

 

[iamkristing]

I corrected the units and still am off. Is the theory/formulas I used correct?

 

[dynamicsolo]

I couldn't say exactly. You only wrote the mechanical energy expression for gravity. What did you use for the value of E? (For that matter, how would you know what to use for E?)

You will probably be better off to do this. Do you know the expression for the velocity of a circular orbit of radius R around a body of mass M? You found a value for that velocity and you know the radius, so you can solve for M from there.