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This Wikipedia article says the the Chandrayaan-2 orbiter will be in a polar orbit above the moon.

The orbiter will perform its mission for one year in a circularized lunar polar orbit of 100 × 100 km.

It takes a lot of energy to change an orbit's inclination near 90 degrees and Chandrayaan-2 does not start off in a polar orbit above the Earth as it would reduce launch windows, as per this Stack Exchange answer. And it would also take more energy because it's most fuel efficient to launch a rocket near the Equator in the Earth's direction of spin (counter-clockwise).

My question: How will Chandrayaan-2 achieve a polar orbit around the moon? eg. Will they change their orbital inclination en-route to the moon? Or will they use a lot of energy and change their orbital inclination while orbiting the moon?

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    $\begingroup$ You just have to make a slight mid-course correction to aim for one of the poles instead of the equator. Then it's just the same as entering an equatorial orbit. Any "orbital inclination" in transit between the Earth and the Moon is small enough to be negligible. $\endgroup$ – TonyK Aug 9 at 17:22
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It will be a combination of things. Like TonyK mentioned in his comments, most of the change will occur during cis-lunar transfer. This is optimal because inter-planetary trajectories can be designed to result in an optimal parking orbit around your target planetary body. One neat trick astrodynamists use is B-plane targeting (a nice AGI article here: http://help.agi.com/stk/index.htm#gator/eq-bplane.htm). I do not know exactly what ISRO did to design these trajectories but I am sure it follows in the same line of reasoning in that since the interplanetary problem is underconstrained, there are multiple parameters engineers can play with to get their desired orbit.

For some reason if the initial inclination of the orbit is not ideal, ISRO could "wait it out" if it is within some margin for the osculating orbit to fall within some tolerance for its orbital parameters. These osculating orbital elements may not be periodic in nature. A good example is polar LEO satellites experiencing something called RAAN drift, where the obliquity of Earth leads to an ever increasing RAAN over time. Obviously if you start off at 0 RAAN, you will naturally end up back there since 360 degrees = 0 degrees, but in a non-spherical body, you will see that these orbital elements will non-linearly effect other parameters including inclination.

Hoping for orbital perturbations to get you into your desired orbit seems a bit naive at first glance (correct me if I am wrong), so you will probably design your entry trajectory to get you where you need to go. Mentioning these perturbations, I think, is neat to know and I am sure very important if you were designing the control systems to maintain your desired orbit.

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