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The Ulysses Spacecraft was sent to Jupiter to change it's orbital inclination via a gravity assist, and enter a nearly polar heliocentric orbit with an inclination of 79° in respect to the solar plane.

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Entering an equatorial LEO in the direction of Earth's rotation requires about 9.4 km/s of $\Delta V$. The amount of $\Delta V$ to enter a Jupiter-Earth transfer orbit requires about 6 km/s from LEO. So I don't see a major problem from a Delta-V budget standpoint to enter a polar LEO, and then escape Earth's gravitational pull to enter a heliocentric orbit.

Question: Why didn't Ulysses, or any future spacecraft intended to study the poles of the Sun, enter a polar orbit around Earth, then fire it's rocket engine to obtain an inclined heliocentric orbit?

Note: Ulysses was launched aboard Space Shuttle Discovery, and the Space Shuttle couldn't enter a polar orbit, but let's ignore this issue as this question isn't specifically about Ulysses but about all polar heliocentric orbit satellites.

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  • $\begingroup$ I think this question is one of the ones that particularly benefits from trying it in Kerbal Space Program. $\endgroup$ – ikrase May 24 at 18:03
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A polar LEO orbit is still a equatorial heliocentric orbit (since that describes the Earth's orbit around the sun).

To change from a equatorial heliocentric to polar heliocentric requires a lot of Delta v.

The final orbit wasn't circular, but we can get an order-of-magnitude figure for the energy required by using the circular plane change approximation.

$$\Delta v_i = 2v \sin \left( \frac{\Delta i}{2}\right)$$ $$\Delta v_i = 60 \text{km/s} \sin(0.69 \text{rad}) = 38\text{km/s}$$

You can get some of that back by not having a final circular orbit. But the change necessary to do the maneuver immediately at the earth's orbit is still quite large.

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  • $\begingroup$ So what would happen if a satellite in a polar earth-orbit burns its engines pro-grade at the night-side of Earth? It would still be in a relatively equatorial heliocentric orbit? $\endgroup$ – Star Man May 23 at 0:16
  • $\begingroup$ Depends on how much of a burn. It's starting in a 30km/s heliocentric orbit around the sun. A "northward" burn of single-digit km/s can get it to escape the earth, but maybe not change the (solar) orbit too significantly. Total energy increases, so orbit would be larger as well. $\endgroup$ – BowlOfRed May 23 at 3:49

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