### Weightlessness in a Satellite-feeling weightless

##### November 23, 2017

# Weightless astronaut-Weightlessness in Orbiting Satellites

In this post we will discuss how does an astronaut feel **weightless** in a nearby orbit and what is the secret behind this **weightlessness** in a satellite?

To start with lets see how we feel this weight. If an object rests on a surface, its weight acts downwards on the surface.

According to **Newton’s third law** the surface also exerts an equal and opposite force on that object.

This is called** reaction force or vertical (normal) reaction force**. This reaction force is responsible for the sensation of the weight felt by the object.

We can sense our weight due to the normal (vertical) reaction force acting on us applied by the surface on which we stand.

## Satellite in a nearby orbit – being weightless

Here we will consider an artificial satellite rotating round the earth in a nearby orbit. **Nearby orbit **is an orbit very close to the earth’s surface.

For this orbit, its *height above the earth’s surface* is negligible for calculation compared to the *earth’s radius*.

We have derived the **orbital velocity** in one of our earlier posts for a nearby orbit.

Orbital velocity for nearby orbit is **v= √(gR)……. (1**)

Now if we consider an astronaut of mass m inside the satellite and analyze the forces acting on him then we find:

**1) His weight mg is acting towards the centre of the earth**

**2) Oppositely directed Normal Reaction force N is applied on him by the surface on which he stands in the satellite**

## Centripetal force for the satellite

Now the resultant of these 2 forces must provide the **centripetal force** F_{c}, which acts on the astronaut as he is in a circular orbit.

So we can write the equation as, F_{c} = mg – N

or,**mv^2/R = mg – N ………….. (2)**

Now importing the expression of the orbital velocity v from 1 to the equation 2, we get,

m.gR/R = mg – N

**or, N = 0 …………….. (3)**

Thus we get that the normal reaction force on the astronaut inside the satellite is zero. Remember that this reaction force is the force which gives us the sense of having weight.

When the astronaut doesn’t sense any such reaction force then he has the feeling of having no weight at all or **being weightless**. This explains the term of weightlessness. In this condition the astronaut will float inside the satellite.

**Related Study: Centripetal Force Orbital Velocity Free Fall Equations Fall against Drag force** **Newton’s third law**