Suppose a nut becomes loose and gets detached from a satellite

[zorro]

Suppose a nut becomes loose and gets detached from a satellite revolving around the earth.
The nut will continue in its orbit due to its inertia. My question is how can an astronaut make it land on earth?

 

[willem2]

An astronaut can't make the nut land on earth. Because such a small object will have a much greater drag compared to its mass, the nut will likely fall back from low Earth orbit in weeks, but will then burn up in the upper atmosphere.

 

[mathman]

Drag depends on altitude, i.e. air density. To make a nut fall to earth, change its velocity vector to point toward earth.

 

[zorro]

How can we change its velocity vector towards earth? If the astronaut throws the nail towards earth, will it land on earth? Or after leaving the satellite, it again follows the orbit due to inertia?

 

[Curl]

Throw it either down or behind him.

Small disturbances will change the orbit radius, until ultimately it will crash into the earth.

 

[pervect]

The best way to deorbit the nut is to throw it opposite the orbital direction - though in practice one couldn't throw it enough, one would instead perform a de-orbital burn.

IF one totally canceled out the orbital velocity of the nut, it'd fall straight down. Without a total cancellation, it'll still enter a lower orbit.

If you restrict yourself to actually "throwing" the nut, you probably won't make a huge difference in its orbit no matter what you do, but you'll maximize the energy loss and minimize the distance of closest approach to the Earth by throwing it behind you, against the direction of orbital motion.