Circular Orbits: Aerospace Engineering Basics

Gravity is a relatively weak force compared, say, to the nuclear forces which hold together atomic nuclei, but nuclear forces operate over short distances, whereas gravity operates over long distances. So, when we’re looking at the motion of objects in the universe at large it’s gravity that’s in control.

The simplest type of orbital motion is just an object moving around a much larger object. For instance, a satellite going around the Earth, or the planets going around the Sun. These orbits are ellipses.

The equation (Circular Motion) is Sir Isaac Newton’s Universal Theory of Gravity. We have two objects with masses M1 and M2. And their centers are separated by a distance R. And so, we have an inverse square law, the force between those two objects falls off as the square of the distance. So, if you move twice as far away you have only a quarter of the gravitational attraction. And then the proportionality constant G is Newton’s Universal gravitational constant (Maybe, throughout the entire universe. -> Still under research)

Quiz Time: Circular Velocity

Let’s consider a satellite in a circular low Mars orbit, 300 km above the planetary surface.

• Radius of Mars = 3396 km
• Mass of Mars = 6.419 * 10²³ kg
• Universal gravitational constant: G = 6.674 * 10-¹¹ m³/kg/s²

What is the orbital velocity of the satellite? Answer should be given in km/s:

Vc² = GM1/R

Vc =√GM/R

G = 6.674 * 10-¹¹ km³/kg/s²

M1 = 6.419 * 10²³ kg

R = 3696 km = 3.696 * 10⁶

Vc = √(6.674 * 10-¹¹ km³/kg/s²)(6.419 * 10²³ kg)/3.696 km * 10⁶

Vc = 3404.56 m/s

Vc = 3.4046 km/s

So, now we can say that this satellite orbits Mars with a velocity of 3.4046 km/s.

Let’s try and figure out how many minutes this satellite needs to orbit Mars once.

There is a simple equation for this:

Circumference formula of a circle / Circular velocity

2πR/Vc

Let’s insert our numbers:

(2 * π * 3696 km) / (3.4046 km/s)

6820.96 seconds -> let’s round it up to 6821 seconds

Answer: The satellite orbits Mars every 114 minutes (6821 seconds).

End

Hopefully, this lesson helped you in gaining some new knowledge on Aerospace Engineering, and in the future, I would like to publish more stories related to this topic.