# Does mass affect orbit size?

My question refers to a capital ship. Ideally, the ship wants to stay as low as possible. Does the mass of the ship affect its possible orbits? If so, what is the lowest orbit possible for this ship? I don't have a number for its mass, but imagine something like the farragut:

Dimensions: Length: 2040m, Width: 806m, Height: 300m

• The mass is not the only number in equation, the speed is the second one. If you can provide enough speed, you can choose any orbit. But because energy for acceleration is relatively scarce, you really aim for the spot that is above the atmosphere. Cover part is irrelevant, as rockets can curve – Antoine Hejlík Aug 21 '17 at 12:38
• No, unless your ship mass is so huge it starts affecting noticeably the orbit of the planet (which is not the case of your "small" ship) – Keelhaul Aug 21 '17 at 12:39
• @AricFowler - if the ship benefits from "line-of-sight" cover, and the intricacies of fuel requirements are neglected - wouldn't it be better to just pick a static point 'behind' the planet and stay there? That way your ship is obscured all the time, not only for a part of its orbit... – G0BLiN Aug 21 '17 at 13:37
• Technically, there's the Roche Limit. But your ship needs to be much bigger before that becomes a problem. – ths Aug 21 '17 at 17:50

Actually, in practice, a very massive object will be able to orbit ad lower altitude than a very light one.

The orbit mechanics is exactly the same (assuming big body mass is still negligible compared with planet).

BUT

It can skim atmosphere fringes and still keep going due to its much larger inertia where a lightweight would be slowed down to a forced reentry.

Of course even very massive objects will be slowed down, but it will take much more time, very likely longer than a space battle will last.

In practice such a massive object can flirt with atmosphere as much as friction won't heat it up too much.

All this is because friction (slow dawn force) is roughly proportional to cross section (square of dimensions) while inertia is roughly proportional to volume (cube of dimensions). You need more time to drag away all energy you gave to spaceship to put it into orbit in the first place.

As I mentioned initially in the comments: no. To the best of my knowledge, the mass of an object only affects how much energy is needed to get that object into a specific orbit. It doesn't affect the actual distance at which that object can orbit. So realistically, the lowest your ship can orbit is just above the edge of the planet's atmosphere. If the planet doesn't have an atmosphere, then you can practically skim across the surface.

• @Keelhaul Got my terminology mixed up, thanks for the correction. – F1Krazy Aug 21 '17 at 12:48
• I would say this is true iff mass(ship) <<< mass(planet) – corsiKa Aug 21 '17 at 19:18

No stable orbits are purely about speed versus altitude.

But an object's bulk dimensions will affect the lowest stable orbit once you get down to atmosphere skimming altitudes, below say 700km. As atmospheric pressure increases larger objects are going the experience more drag at a given altitude than smaller ones. Heavy objects have greater inertia and are less affected by a given amount of drag so it really comes down to object density and how much fuel you're willing to burn to maintain an inherently unstable position once you get down that low.

You didn't mention ship mass so I would estimate it as 100 million tons(10^11 kg).

If I would take you question literally then first thing I would think of is offset of barycenter. Basically if you make two bodies of equal mass orbit each other then they rotate around center of their masses that is right between them. If one body is lighter then barycenter would move towards heavier body.

Earth weights 6*10^24 kg, you ship weights 60 millions million times less, so barycenter would move only 1/10 000 of mm from Earth center of mass. Earth gravitational anomalies would affect orbit of the ship much more than that.

But I suppose you mostly care how much atmosphere would affect orbit. Obviously, the bigger the ship, the less surface to mass ratio, so atmosphere affects it less and less. Usually satellites don't go below 300 km, but a ship this big can go much lower, especially for short time.

Calculations are relatively simple. Air resistance force would be 1 / 2 * Cx * p * V^2 * Sx, p - air density, V - ship speed(~= 8 km/s), Sx - front surface(Width: 806m, Height: 300m = about 2.4*10^5 m^2), Cx - resistance coefficient(= 2, because speed is so big that we can consider that all interactions are inelastic). So it simplifies to 2.4*10^5 * 6.4*10^7 * p ~= 10^13 * p

At 100 km density is about 5*10^-7 kg/m3 so resistance would be 5*10^6 N = 500 ton(2 kg per m^2). Ship would decelerate 0.05 mm/s^2, and lose only about 0.27 m/s per revolution. 1 meter per second on LEO corresponds to roughly 2 km of orbit height so it would lose 0.5 km of height per rotation. But deceleration would speed up quickly as air density grows exponentially, so it would go down after 10-20 revolutions. Or you can accelerate ship with engines accordingly - 0.05 mm/s^2 is nothing for battleship.

But as ship slows down it loses energy. According to energy conservation this energy should go somewhere - it turns to heat. That would be about 100 KWt per m^2, that's enough to burn small parts like antennas and make ship look very bad.

If you move it a little higher - 120 km, air density becomes 4 times less, 140 km - 60 times less. So at 140 km it would lose only 100 meters per revolution and external parts should be OK, though I think paint would suffer.

tl;dr

Below 100 km heat from air resistance becomes too much and orbit decays too quickly. But if you have appropriate(force shield?) protection and powerful engines you can go as low as you want.

At about 150 km heat is not a big problem and a ship that big can orbit for days even without turning engines on. At 200 km and above air is not a problem for such ship.

Once the ship is in orbit, if it's going fast enough, it will stay in orbit. The only problem is the atmosphere. If the ship in question is too low, then drag comes into play, slowing the ship down, and making it fall out of orbit. Then you have to have the engines on to keep speed up. Otherwise, there shouldn't be any problems

• Welcome to Worldbuilding, Chris! If you have a moment, please take the tour and visit the help center to learn more about the site. You may also find Worldbuilding Meta and The Sandbox useful. Here is a meta post on the culture and style of Worldbuilding.SE, just to help you understand our scope and methods, and how we do things here. Have fun! – Gryphon Mar 6 at 15:56