Calculating an eccentric enough orbit to allow a dip into atmosphere and escape again

Question

How would I calculate if it is possible to have an eccentric enough orbit around a gas giant to dip the periapsis some depth(how deep?) into the atmosphere of a gas giant like Jupiter or Saturn and taking into account the atmospheric drag, still escape to a stable orbit? Is this even possible or is there a calculator online that might help?

CLARIFICATION I intended this to be a one time pass through with a man made ship or probe. Sorry for the confusion.

I want to use a story element where a spacecraft is setups up a high enough apoapsis to have the momentum and orbital velocity so they can "dive" into the planet's atmosphere to whatever depth is possible and have the energy to get back out to space. I can allow for them to add to the speed at Periapse if needed but I wanted to determine how deep they could dive and still get out with a margin of safety.

Answer 1

Technically, yes, but probably not how you’re envisioning.

If what you’re picturing is a craft dipping far enough into the atmosphere to look like it’s “in the clouds,” so to speak, and then exiting again back into space, then probably not.

However, you may be able to achieve something that at least somewhat resembles what you're imagining. Here's some factors worth considering:

It sounds like you need your craft to be in orbit for a while before it performs this maneuver. If instead you want your object to originate from someplace outside the immediate system (e.g., launched from another planet) and directly descend into the atmosphere once it arrives, then essentially what you're describing is an extremely dramatic version of aerocapture.

Either way, the key here is drag. Notice that with an aerocapture maneuver, the portion of the atmosphere targeted for increased drag is still extremely thin. This is because, at orbital velocities, just a tiny amount of gas molecules is enough to cause a whole lot of heat and friction. So, to a casual observer, craft undergoing an aerocapture maneuver do not appear to be noticeably “inside” any perceptible gaseous medium.

If you absolutely need to construct a craft that is able penetrate deep into the atmosphere of a gas giant at orbital velocities and then exit, then it would need to be:

1. traveling an order of magnitude faster than satellites typically travel, in order for atmospheric drag not to slow it down below escape velocity;
2. composed of magic space-metal to withstand the extreme heat.

If your craft is originating from outside the immediate system, then as long as it’s traveling fast enough to maintain atmospheric escape velocity, but slow enough not to exceed orbital escape velocity (and it doesn’t vaporize from the heat), then, yes, you could theoretically perform an insertion maneuver this way. Alternatively, if your craft must perform this dive from an already-stable orbital position around the planet, it would need a crazy amount of thrust to begin the maneuver. (E.g., you include some propulsive means on the craft strong enough to boost the object back up to an appropriate speed or altitude. But again, the thrust needed would be enormous.) Otherwise, you'd just be initiating a skip reentry.

In both cases, it all depends on the aerodynamics of the craft, the atmosphere of the planet, the altitude and speed of the craft, and so on. There are many variables.

Answer 2

Consider the Orbital Mechanics Wikipedia article, particularly the fourth main bullet point under Rules of Thumb: "If thrust is applied at only one point in the satellite's orbit, it will return to that same point on each subsequent orbit, though the rest of its path will change. Thus one cannot move from one circular orbit to another with only one brief application of thrust." This is enough to show that what you want is not possible as you state it.

The last thrust applied to the spacecraft is from the drag of the atmosphere. That means that the resultant orbit will go through the atmosphere again, and the spacecraft will continue to do so on each orbit until it has decayed to the point that more of the orbit is in the atmosphere. There is no stable orbit that goes through the atmosphere.

There are two ways to get around this. One is to keep escape velocity after leaving the atmosphere, so the spacecraft returns to deep space and hence is not in an orbit. The other is to accelerate at the high point of the orbit, which will raise the low point, and that can remove the orbit from the atmosphere.