Projectile motion inside International Space Station (ISS)

PROJECTILE MOTION INSIDE INTERNATIONAL SPACE STATION

INTRODUCTION

Projectile motion is a form of motion that follows or traces out a parabolic path. The predominant reason for the origin of projectile motion is acceleration due to gravity. When an object is simply given a horizontal initial velocity, gravity which is always acting downward will exert a vertical pull on the object. The resultant of horizontal and vertical components is a parabolic motion. The magnitude of horizontal and vertical components may or may not be equal since it depends on the angle of trajectory. However both horizontal and vertical components are totally independent of each other. In this post, we intend to determine time of flight, maximum attainable height and maximum attainable distance of an object undergoing projectile motion inside the International Space Station (ISS).

ASSUMPTIONS

1. Air, wind and other frictional resistance are neglected

2. Temperature effects do not impede the motion

3. The ground surface is perfectly horizontal

4. The projectile moves along a two dimensional path

CALCULATION

Consider an object of mass ‘M’ kg, moving with an initial velocity ‘u’ at an angle ‘θ’ with respect to the horizontal. Let ‘g’ be the acceleration due to gravity on ISS. It is important to note that projectile motion is independent of the mass of the object in a vacuum. However in air or other media, the drag coefficient being different for various object shapes and sizes, it is no longer independent of mass. The ISS is always in a state of free fall, hence experiences weightlessness. Thereby all the objects inside the ISS will also experience weightlessness. Hence it is safe to assume that the acceleration due to gravity is zero.

The equation of projectile motion in this case is given by,

where,

h – Horizontal distance at which the projectile attains maximum height (m)

k – Maximum height attained by the projectile (m)

a – Focal length of the parabola (m)

A projectile motion is represented in figure.1 with all the coordinates

Fig .1 A projectile motion

Now, the other aspects of the parabolic motion such as total time taken, maximum height and maximum distance attained will be discussed

The time of flight ‘T’ is given by,

where,

T – Time of flight or total time taken (s)

u – Initial velocity of projectile (m/s)

θ – Angle of projectile (degree)

g – Perceived acceleration due to gravity inside ISS (0 m/s²)

The value ‘ꝏ’ or ‘infinity’ implies that the projectile motion will never be completed because due to lack of gravity, the projectile will continue to move at 45° rather than falling down to the surface.

The maximum height attained (H) by the object is given by,

The value ‘ꝏ’ indicates that the object will never achieve any maximum height since the projectile will always keep moving upward at the launch angle instead of falling down.

The maximum distance attained (d) by the object is given by,

The value ‘ꝏ’ indicates that the object will never achieve any maximum distance since the projectile will always keep moving upward at the launch angle instead of falling down.

Equations (3), (5) and (7) indicate that projectile motion cannot be completed inside the ISS since it is always in a state of free fall.

CONCLUSION

Thus it can be observed from the calculations that the projectile motion can never be completed inside the ISS.