An expeditionary force, let us say, has set forth from Mars, heading toward Earth. Its mission is to establish and enforce a blockade of Earth - or of the rest of the Solar System, depending on how you look at it. Specifically, certain persons are to be embargoed, forbidden to travel from Earth. to any other planet, moon, or other astronomical body. Travel to good old Luna may or may not be included in the embargo, depending as much on operational as policy-objective considerations. (See below!)
Violators are subject to arrest. If they resist arrest they may be fired upon.
We will not, for this discussion, trouble ourselves with who 'certain persons' are, or why someone on Mars wants to keep them from leaving Earth. For our purpose, it is sufficient that
a) The relevant Earthside authorities have zero interest, or less than zero, in helping Mars bottle these certain persons up. A polite request would reach Earth a lot faster, easier, and cheaper than an expeditionary force. But a polite request, by itself, would be ignored.
b) Somebody on Mars (or at least in Mars space) has means and motive to issue more than a polite request. Namely send the expeditionary force.
c) Whoever this somebody is, their objective is to control outbound traffic from Earth, not eliminate it - especially not permanently. Slagging Earth, its launch sites, or orbital infrastructure are not objectives, or even acceptable outcomes. Slagging individual transport-class ships is dicey, depending on the circumstances. Military craft, however, are fair game.
Human interplanetary travel uses electric propulsion, on the general lines often discussed here. Main drive acceleration is in the milligee range, and the ships have either very large radiator fins or very large solar wings. Hardening these is a nonstarter, so deep-space ships are inherently vulnerable.
On the other hand, punching a few small holes in the wings will not cripple them, so the vulnerability should not be overstated. Spaceships won't sink, or become aerodynamically unflyable.
Delta v will be a constant preoccupation of commanders. This has been discussed here before, but it is almost impossible to overstate. The Martian expeditionary force probably take a slower orbit than civil transports, because transports can refuel at their destination. The expeditionary needs to reserve propellant for a (slow!) abort orbit back to Mars.
And while milligee drives preclude 'tactical' maneuver, at least some of your deep space ships likely have a few km/s of delta v for 'operational' orbit changes in Earth space. At a rate of about 1 km/s per day. By bringing along plenty of tankers for support, a few ships might have a couple of dozen km/s for operational movement.
Chemfuel spacecraft can have pretty much as much acceleration as you want, but unless they start out as mostly propellant drop tanks they will carry only 2-3 km/s of delta v. Which means that a 1 km/s burn is huge, a sizable chunk of your entire maneuver capacity.
Nuclear thermal propulsion is intermediate, but much closer to chemfuel. And for human missions much of the advantage may be lost due to shielding mass.
Just on a practical level, all of these constraints are a good reason to seek mutual understanding through dialogue. But of course you won't.
On the flip side, the technology of deep space travel makes 'distant blockade' a surprisingly viable concept. Departing ships spiral out for a week or more, their orbital speed (relative to Earth) gradually decreasing to a couple of km/s, before they finally pass escape velocity and break loose into solar orbit.
This gives ample time for ships in high Earth orbit to intercept would-be blockade runners, the interception taking place somewhere between geosynch and lunar distance. This sort of space chase is more than a bit odd to contemplate. Both prey and pursuer are circling Earth throughout the chase, which unfolds over a period of days due to their extremely sluggish acceleration.
But the scope for evasive maneuvers is extremely limited, since the blockade runner must keep spiraling outward if it is to proceed on its journey. One possible tactic is to feign a departure, either to draw the blockader into battle with a heavily armed ship, or as sheer bluff - forcing the blockader to expend its limited propellant, then 'reverse course' and spiral back inward toward low orbit. The ship performing the bluff has also expended propellant, but it can refuel at LEO, an option not available to the blockaders.
Such peculiar chases are complicated by the possibility of chemfuel (or nuke thermal) ships - or munitions - making far more abrupt orbit changes, leading to an engagement in a matter of days.
Earth-Moon travel is, or can be, entirely different, carried out using chemfuel or nuke thermal propulsion, blasting straight out of LEO into the lunar injection orbit. The challenge of intercepting Moon-bound ships is equally different, to the point that the blockader will either have to make separate provision for it (a ship positioned at the lunar L1 point, or in lunar orbit), or else not attempt to enforce the blockade with respect to Luna.
If blockade runners were pre-parked in lunar orbit - and the Earth-based defender had months to position them, while the blockader was en route from Mars - then the blockader must extend enforcement to lunar space. Otherwise the blockade might be evaded simply by going to lunar orbit first.
So far I have said nothing about weapons. The scenario as described does make one negative presumption: that lasers (or whatever beam weapons) have an effective range less than about 50-100,000 km - whatever turns out to the the distance from Earth at which departing electric ships reach escape velocity and transition from geocentric spirals to their solar transfer orbits.
Otherwise the prime intercept zone lies within direct zapping range of lasers in low orbit - or even on the ground. In that case the expeditionary force must either engage in a direct laser battle, or blockade from a higher orbit, outside the range of 'shore guns.' Intercepting blockade runners then becomes more difficult and propellant-costly, since they are already above Earth escape velocity on outbound solar orbits.
Kinetics, or missiles generally, have no 'range.' If they are on orbits below escape velocity they will orbit Earth (or Luna) indefinitely; if above escape velocity they will head out into the void on solar orbits. More relevant for missiles is flight time, which defines the target's window for engaging the missile or evading it.
Electric ships can, potentially, outrun any chemfuel or even nuke thermal missiles by running them out of delta v. But with milligee acceleration they can only do so if the flight time is in days. The drawn-out evasive maneuver will cut fairly deeply into reserve delta v, and leave the target far from its previous orbit, therefore probably off station.
I have also said nothing about the ships involved, save that they have the broad characteristics determined by their propulsion. It is by no means a given that either side has craft that fit our image of warships, especially if lasers or other beams are not an important factor. The expeditionary force must come closer, since its deep space craft must be able to deploy weapons in some way. But the Earth-based defender might well rely entirely on missile buses pre-positioned in patrol orbits, with its ships providing purely logistic support.
Finally, bear in mind that the scenario outlined - distant blockade - is pretty much the most favorable for an expeditionary space force. The blockader is not seeking to land anywhere in force, or even contest control of Earth's inner orbital space, only interdict outbound deep space traffic. It need not come close enough to Earth to be at risk of short-warning attack by surface-launched ASATs or surface-based lasers.
Related Links: Atomic Rockets, of course - especially, but not exclusively, the pages on space warfare.
And previously in the Space Warfare series on this blog:
I: The Gravity Well
II: Stealth Reconsidered
III: 'Warships' in Space
V: Laser Weapons
VI: Kinetics, Part 1
VII: Kinetics, Part 2 - The Killer Bus
VIII: Orbital Combat
IX: Could Everything We Know Be Wrong?
X: Moving Targets
XI: La Zona Fronteriza
XII: Surface Warfare
XIII: The Human Factor
XIV: Things As They Ought To Be
XV: Further Reflections on Laserstars
XVI: Origins and Scratch Forces
Also ... Battle of the Spherical War Cows: Purple v Green
Further Battles of the Spherical War Cows
Plus Space Fighters, Not Space Fighters, Reconsidered?
And, indulging in heresy - Give Peace a Chance
The image, as so often, comes via Atomic Rockets. Note that the engagement shown is much closer to the planet than the intercept zone discussed in the post.