Orbit


 

To reduce the load on the active cooling system of “Millimetron” observatory telescope and to provide an unprecedented high angular resolution, its orbit is located in the vicinity of the libration point L2 of the Sun-Earth system, at a distance from the Earth of 1.5 million kilometers away from the sun. Spacecraft excretion is supposed to be done using the heavy class rocket carrier.

“Spektr-M” spacecraft flight program is divided into three stages:

  • Excretion into an intermediate orbit;

     

  • Spacecraft flight to the libration L2 point vicinity;
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  • Maintainingthe operational orbit for scientific observations.
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Ballistics calculation and support ofthe flight was conducted in the Ballistics center of the Keldysh IPM, RAS. Calculations were done assuming the perfect navigation and absolutely accurate performance maneuvers. At this stage of “Spektr-M” project development (“Millimetron” observatory) adopted a single-pulse scheme of spacecraft injection into the working orbit.

Parameters of halo orbit version around L2 point:

  • Maximum spacecraft yield from the ecliptic plane – 910 thousand km

  • Halo orbit period – 180 days;

To represent the trajectory of the spacecraft motion relative to the point L2 introduced in consideration a rotating in time right rectangular coordinate system (CS) LXYZ. At each instant moment of time the center of this CS (L point) coincides with the point L2, X-axis is directed to the center of mass of the Sun, the Z axis is perpendicular to the ecliptic plane and directed towards the world North Pole.

Figure 1 – Preliminary scheme of spacecraft excretion to vicinity of L2 point.

Figure 2 – The projection of flight trajectory ofthe halo orbit on the XY plane of rotating CS (origin at the L2 point, dimension-thousand kilometers).

Figure 3– The projection of flight trajectory ofthe halo orbit on the XZ plane of rotating CS (origin at the L2 point, dimension-thousand kilometers).

Figure 4– The projection of flight trajectory ofthe halo orbit on the ZY plane of rotating CS (origin at the L2 point, dimension-thousand kilometers).

For small deviations of the orbital parameters from the required values, spacecraft quickly leaves the reference orbit (Figure 1), because of its instability. Therefore, the motion of spacecraft in the vicinity of the reference trajectory will be maintained through active controlling system by periodic corrections of the trajectory parameters. To maintain the spacecraft orbit around unstable point L2 during the year it is required to carry out about 8-10 corrections with a total incrementvalue for characteristic speed of about 10m/s. Given the inevitable errors issuing corrective impulse and knowledge of the spacecraftposition in conditionally periodic orbit around L2 point of the Sun-Earth system, we can assume that the trajectory correction should be done about 12-18 times during a year of flight.

Figure 5 – Direction “Earth-Spacecraft” vector.