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According to Wikipedia, the MRO has an orbital period of 112 minutes:

In September 2006 MRO fired its thrusters twice more to fine-tune its final, nearly circular orbit to approximately 250 to 316 km (155 to 196 mi) above the Martian surface, with a period of about 112 minutes.

However, it also says that the MRO completed a second burn in 2015 which lasted 75 seconds. Did this burn change its orbital period at all?

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I went to JPL Horizions and extracted the osculating elements for MRO about Mars at 1 day intervals over the last ten years or so. Osculating elements are not exactly Keplerian elements, but they are close. They are really the instantaneous fit to the cartesian state vectors $x, y, z, v_x, v_y, v_z$ produced in the integration for the ephemeris. Every little perturbation due to gravity from all solar system bodies, Mars' uneven gravity field, and all other effects cause tiny departures from simple Keplerian orbits and so look like noise in the osculating elements.

I've plotted the daily period and a 100-day running average of the period as a function of year. It looks pretty darn steady!

I don't see any evidence of a permanent change in the period after the 2015 even that you mention.

I've also included a dump of all twelve osculation elements (days since 01-Jan-2017) for kicks. You can see a roughly 700 day oscillation in MRO's inclination.

I've also included the header at the end, it may have some interesting information for you. It's fairly long, don't forget to scroll up and down.

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Revised: Jul 10, 2017    Mars Reconnaisance Orbiter (MRO)  / (Sun)         -74
                               http://marsprogram.jpl.nasa.gov/mro/
 UPDATE (2014-Jun-10):
  C/2013 A1 (Siding Spring) will have its closest approach to Mars on Oct 19,
  2014 at a distance of about 135,000 km.

  Location of predicted MRO minimum risk from comet particles
  (occultation mid-point):

  Latitude: 7.6083 deg
  Time:     19-OCT-2014 20:08:07.182392952 ET (CSS CA + 98 min)

 MISSION LAUNCH DATE:                                         MARS ARRIVAL DATE:
  Aug 12, 2005 11:43 UTC (it's up and away)                   March 10, 2006
  Notes:  Aug 10, 2005: Original launch was scrubbed (gyros
          Aug 11, 2005: Second attemped was launch scrubbed (fueling sensors)
 LAUNCH VEHICLE:
  Atlas V two-stage. Separation from Centaur: 2005-Aug-12 12:40:51.68 UTC

 BACKGROUND:
  MRO aerobraked for 6 months from the post-insertion 35 hour orbit, saving
  450 kg of fuel. Primary science phase starts in November of 2006 and
  nominally operates for 2 Earth years from a 112 minute, near circular polar 
  orbit. 
 SPACECRAFT PHYSICAL PROPERTIES:
  Height=  6.5 m                          Solar panels =   20 m^2
  Width = 13.6 m (tip-to-tip)             launch weight= 2180 kg

 SPACECRAFT TRAJECTORY:
  Trajectory starts after Centaur launch stage separation (cruise phase).
  Trajectory after 2017-Jul-03 is PREDICTION.

  Trajectory files (from MRO Nav., JPL)      Start (TDB)         End (TDB)
  --------------------------------------  -----------------  -----------------
  mro_cruise                              2005-Aug-12 12:42  2006-Mar-10 22:06
  mro_ab                                  2006-Mar-10 22:06  2006-Sep-12 06:40
  misc reconstruction (mro_psp1-42)       2006-Sep-12 06:40  2017-Apr-01 01:01
  mro_psp_rec                             2017-Apr-01 01:01  2017-Jul-03 23:16
  mro_psp                                 2017-Jul-03 23:16  2017-Aug-07 14:12

*******************************************************************************
Ephemeris / WWW_USER Wed Oct  4 20:17:49 2017 Pasadena, USA      / Horizons    
*******************************************************************************
Target body name: Mars Reconnaissance Orbiter (spacecraft) (-74) {source: MRO_MERGED}
Center body name: Mars (499)                      {source: mar097}
Center-site name: BODY CENTER
*******************************************************************************
Start time      : A.D. 2005-Aug-13 00:00:00.0000 TDB
Stop  time      : A.D. 2017-Aug-07 00:00:00.0000 TDB
Step-size       : 1440 minutes
*******************************************************************************
Center geodetic : 0.00000000,0.00000000,0.0000000 {E-lon(deg),Lat(deg),Alt(km)}
Center cylindric: 0.00000000,0.00000000,0.0000000 {E-lon(deg),Dxy(km),Dz(km)}
Center radii    : 3396.2 x 3396.2 x 3376.2 km     {Equator, meridian, pole}    
Keplerian GM    : 4.2828373620699087E+04 km^3/s^2
Output units    : KM-S, deg, Julian Day Number (Tp)                            
Output type     : GEOMETRIC osculating elements
Output format   : 10
Reference frame : ICRF/J2000.0                                                 
Coordinate systm: Ecliptic and Mean Equinox of Reference Epoch                 
*******************************************************************************
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That burn used the "intermediate thrusters", 6 units producing 22 N force each, for a total of around 10000 newton-seconds of impulse.

I was able to coax Wolfram Alpha into admitting that, against a mass of about 1300 kg, this corresponds to a delta-v of about 7.8 meters per second, which is about 0.2% of the 3415 m/s average orbital velocity expected.

Depending on how this delta-v is applied, it could increase or decrease the period, or leave it unchanged; if it was used to put the spacecraft into a slightly higher, slower orbit, the period could increase from 112.6 minutes to 113.4 minutes. (I see from @uhoh's answer that the actual period is a bit shorter; I'm using spherical-cow figures here.)

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    $\begingroup$ Two really good answers; unfortunately, I can only accept one. $\endgroup$ – Phiteros Oct 5 '17 at 19:24

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