What is the limit to how many satellites can orbit the earth?

Question

I would like to know how many satellites are physically able to be in place, at the same time, orbiting the earth. Lets ignore which Nations need or use the most satellites (area in space above them) and assume an even distribution. My understanding is each satellite is inline with a degree on earth (longitude), but there are only 180 of these. Would you then be able to line up satellites on each degree of latitude for each degree of longitude? So 180 x 180 = 32400? Or is there more to this? Could you put a satellite either further or nearer to the earth so they would almost overlap to make room for more?

Answer 1

This is actually quite a complex problem. At large numbers of satellites, gravitational effects need to be considered. A real answer would need values such as 'every satellite has the same mass and volume' etc. Basically you can keep adding satellites until Earth becomes a black hole. Satellites are very dense since they have lots of metal (which is a dense material) In my opinion, a great 'answer' to this question would be a fun computer simulation.

If we just use the values given by Phil H, we fit in satellites between 2000 km and 35786 km altitudes. $R_E$, the radius of the Earth is 6371km. So we calculate the volume: $V_{total}=\frac{4}{3} \pi [(d_2+R_E)^3-(d_1+R_E)^3]=\frac{4}{3}\pi (42157^3-8371^3)=9.341\times10^{14}\,\text{km}^3$

We assume that all the satellites have mass of $m_s = 800\,\text{kg}$ (note that this is a 'fantasy' problem so we don't really need to follow real world statistics) and volume $V_s=4.8 \,\text{m} \times 4.8 \,\text{m} \times 5.5 \,\text{m} = 1.267 \times 10^{-7} \, \text{km}^3$

Thus, the total mass of the orbiting satellites will be $M_{total} = \frac{m_s}{V_s} V_{total}= 5.90 \times 10^{24}\,\text{kg}$

Now let's compare that to the mass of the Earth, $M_E=5.97\times 10^{24} \,\text{kg}$.

Notice how $M_{total} \approx M_E$, though this is just due to some values which we chose and does not arise from some values which arise from nature.

Answer 2

Satellites are very small, so there would have to be an enormous number to use up the 'space' available.

You mention lattitude and longitude which suggests an explanation of LEO and GEO (Low and Geostationary Earth Orbits) would help. in Geostationary orbit (e.g. TV satellites), the satellite orbits at a specific distance so that it's always in the same place in the sky, as its orbit is then 24 hours long. This special orbit runs around the equator, as any other inclination would make it move in the sky, in a figure of eight.

In a lower orbit, the satellite appears over the horizon, zips across the sky and disappears again. This is why GPS systems don't have an antenna or dish that you point at one place, as GPS uses a constellation (group) of many satellites at 20,200 km altitude.

So the available space for satellites extends from Low Earth Orbit (2,000 km up), e.g. telecomms satellites and Hubble, out to the moon, which is our only natural satellite. Mostly they stay between LEO and GEO (35,786 km altitude).

Having said all that, the more we put up there, the more junk we end up with as pieces fall off satellites, or they collide, or they are hit by other space junk. This is increasingly a concern as early missions largely assumed everything would end up burning up in the atmosphere eventually.

The space available for satellites, then, is very large. Even in a single LEO orbit there is more 'space' than the distance around the equator. The Geostationary orbit has a limited number of spaces available by international agreement to prevent collisions or interference.