SpaceBanter.com - View Single Post - Orbital mechanics question DSCOVER L1 orbit

**Jeff Findley[_6_]** · February 16th 15, 04:49 AM posted to sci.space.station,sci.space.policy

In article ,
lid says...

On 15-02-15 17:15 , Jeff Findley wrote:
In article om,
says...

On 15-02-14 04:04, someone wrote:

URL:
http://seattletimes.com/html/businesstechnology/2025669167_apxscideepspaceobservatory.html

Based on that article, stage 2 left DSCOVR in a elliptical orbit around
earth, with 37° inclination and 1,2 milion km * 187km orbit.

Would it be correct to state that L1 is an orbit around the sun, but at
a speed that matches Earth's orbit around the sun despite being at a
lower orbit than the Earth, which is made possible by Earth's gravity
compensating. ?

It looks like an orbit around the sun, but it's not.

It is, in the geometrical sense: the L1 locus follows an (approximately)
closed, nearly circular path with the Sun close to its centre. Orbital
period = 1 Earth year.

But, the velocity is *wrong* for an orbit at that distance from the sun
(in the sun frame of reference). The velocity is also *wrong* for an
orbit at that distance from the earth (from the earth frame of
reference). It's not truly in an orbit around either body.

It's correct to
state that L1 is the location in space where the gravitational forces on
a satellite from the sun and the earth cancel out.

No, if the forces cancelled, then an object placed in L1 would move in a
straight-line path. Instead, it follows an orbit around the Sun, which
means that there is a net gravitational acceleration towards the Sun.

As JF Mezei said, at L1 the gravitational attraction between the Earth
and the satellite counteracts not all, but just enough of the
gravitational attraction between the Sun and the satellite to increase
the orbital period of the satellite from its sans-Earth value (less than
one year) to one year, thus making it keep pace with the Earth.

True, but one could say it *exactly* the same thing, but replacing the
earth with the sun and vice-versa. In other words, in the earth frame
of reference, it also goes around the earth once a year.

This is a three body problem. The terminology reserved for the two body
problem does not exactly apply because the two body equations don't work
for this three body problem.

Jeff
--
"the perennial claim that hypersonic airbreathing propulsion would
magically make space launch cheaper is nonsense -- LOX is much cheaper
than advanced airbreathing engines, and so are the tanks to put it in
and the extra thrust to carry it." - Henry Spencer