Re: Does any of the earth's atmosphere escape into space?

Here are some answers to your question!

1) Yes molecules are "attached" to Earth by gravity, but there is an interplay with velocity of the molecule. In order to escape the Earth's atmosphere, a molecule or a rocket or anything needs to have a certain velocity. The escape velocity depends on gravity and so on the mass of the planet: v_escape = square root(2GM/R) where G is the universal constant of gravitation, M is the Earth's mass and R the Earth's radius.

The atoms and molecules in the atmosphere have a velocity, and their most probable velocity (Maxwellian distribution) depends on the temperature and the particle's mass: V_probable = square root (2*k*T/M). where k is Boltzmann's constant, T is the temperature of the atmosphere, and m is the mass of the atom or molecule. If you work this out for the temperature of the upper atmosphere, it shows that hydrogen and helium will escape, because for them v_probable > v_escape. In fact, you can go through this exercise to see which planets should have which gases. This explains why only the giant planets have hydrogen and helium in their atmospheres.

2) Only a VERY tiny amount of the atmosphere is leaking off into space. In light of #1) some mechanism is need to give the heavier atoms or molecules additional energy to reach the escape velocity. This can happen, for example by collisions with particles from the solar wind. Another way for particles from the atmosphere to escape is if a hydrogen or helium atom is produced. This happens, for example, when an ultraviolet photon from space hits a water molecule and breaks it up. There are other thermal and non thermal processes that can impart enough energy for other molecules to escape. However, the amount of gas leaving the Earth is very, very small. It is roughly estimated to be 10^8 atoms per cm^2 per s. If this rate had been the same for 4.5 billion years (the Earth's entire existence) this would be equivalent to water covering the Earth's surface to a depth of a metre. By comparison the water in the oceans today is equivalent to an average depth of 3 km.

3) There are indeed processes on Earth contributing to the Earth's atmosphere such as volcanoes contributing CO₂, water vapour from the oceans. But just as water vapour returns to Earth as precipitation, there are cycles for CO₂ returning back to the Earth's crust such as limestone formation. In this respect you have to realize that the gases being added to the atmosphere are not lost almost entirely by returning to Earth, hardly at all by dissipation into space. You should be able to find out about the details of the different cycles that add and remove gases to the atmosphere, including rates for some aspects of them in a senior high school or college level textbook. There are too many details to explain here! Of course today there is a net increase in certain gases in the atmosphere from the large amounts of fossil fuels being burned, and these are contributing to the greenhouse effect. Unfortunately those gases are not "leaking out into space".

4) Finally, Mars's and the Earth's atmosphere have evolved from their initial state into what they are today. So when you have heard that Mars's atmosphere was more dense in the past, it was likely referring to shortly after the formation of the planets when large amounts of hydrogen and helium were escaping the inner planets' atmospheres. You can read about this evolution in a college level astronomy text book.