[AR] Re: OT: Hohmann Transfers
- From: Henry Spencer <hspencer@xxxxxxxxxxxxx>
- To: Arocket List <arocket@xxxxxxxxxxxxx>
- Date: Wed, 9 Feb 2022 11:04:46 -0500 (EST)
On Tue, 8 Feb 2022, Carl Tedesco wrote:
All the internet sources I could find say that the Perseverance rover
travelled to Mars via a Hohmann transfer. Using a Sun-Earth distance of
149.6 million km and a Sun-Mars distance of 228 million km, I calculate
that the transfer should take ~259 days. ... 259 vs 204 days? Why the
discrepancy? Was some sort of modified Hohmann transfer used?
The Hohmann transfer is an idealized case. Reality is not so simple.
There are minor complications from the two planets' orbits not being in
quite the same plane.
There are major ones from Mars's orbit being significantly elliptical --
Mars's distance from the Sun varies from about 207Mkm to about 250Mkm.
(That's the main reason why some Mars launch windows are better than
others.) Earth's orbit isn't perfectly circular either, although the
range is much narrower.
A spacecraft that's going straight into Mars's atmosphere for aerodynamic
deceleration to landing, may be willing to accept a slightly higher
arrival velocity in return for needing less boost for Earth departure --
the effective Isp of aerodynamic braking is much higher than that of
chemical rockets. (Whereas an orbiter that has to expend fuel for braking
cares a lot about minimum arrival velocity, especially since its
propulsion system will often have lower performance than the launcher's
final stage.)
The *date* of arrival can also matter somewhat, given communications
constraints and the like -- e.g., the spacecraft doesn't want to arrive
when Earth is almost exactly on the other side of the Sun and hence can't
communicate.
There can be constraints on the departure end too, e.g. limits on what
launch directions are permitted due to range-safety issues, availability
of tracking, etc.
Finally, you want the launch window to be substantial -- preferably weeks,
not days -- in case there are last-minute delays due to weather or
hardware problems. That typically means that when nothing does go wrong,
the launch is significantly earlier than the exact optimum date.
So it's actually a fairly complicated optimization problem, with the
characteristics of both the launcher and the spacecraft figuring into it.
Not too surprising if the results typically don't match the ideal case.
Henry
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