Launching a satellite into orbit requires consideration of a number of major science ideas. These include gravity, circular motion and atmospheric drag.

Atmospheric drag

Satellites need to be placed in orbit high above the Earth’s atmosphere so that the drag of the atmospheric gases doesn’t make the orbiting satellite slow down.

A good minimum height for a satellite is 100 km above the Earth’s surface. This is the official definition of space (the Kármán line) because there are so few gas particles above this altitude. However, most satellites are placed into orbit between 500 and 1500 km.

There is gravity in space

A lot of people think that there is no gravity above the Earth’s atmosphere. The truth is that gravity keeps pulling an object towards the centre of the Earth even if the object is far above the Earth’s atmosphere. The force of gravity pulling you towards Earth at an altitude of 100 km compared to that acting on you if you were on a 10 m high diving board only varies by about 20 N.

We know this from Newton’s universal law of gravitation, which takes the form

F = G mEmO/d2

where

F = force of gravity in newtons

G = the universal gravitation constant

mE = mass of the Earth

mO= mass of the object

d = distance between the object centres.

Using this formula shows that the force of gravity acting on a 70 kg person on a 10 m diving board is 688 N compared to 667 N for the person at an altitude of 100 km above the Earth’s surface.

Energy needed to reach an altitude of 100 km

The work that needs to be done on a 1 kg object to reach a height of 100 km above the Earth’s surface is calculated in the following way.

work done = gravitational force x vertical height

= (1 x 9.8) N x (100 x 1000) m

= 980,000 joules

If we account for the fact that gravity is decreasing very slightly as distance from the Earth increases, the corrected value is 967,000 joules.

To supply this amount of energy per kilogram of load, you would need a very powerful and well designed rocket. Since the rocket and fuel also have mass, there needs to be additional fuel to lift the mass of the fuel and rocket into space.

But there is still a huge problem. Even though this 1 kg mass has reached space, it would still fall back to Earth because there is still a very strong pull of gravity attracting it towards the centre of the Earth.

Speed of orbit

To balance the strong gravitational pull, the 1 kg mass must be given additional energy to place it in orbit around the Earth. An object will fall back to Earth unless it has enough orbital speed.

To calculate the orbital speed needed, we combine Newton’s law of universal gravitation with a circular motion equation. The net result of this is an equation of the form

V=√[(G x ME)/R]

where

V = orbital speed

G = the universal gravitation constant

mE = mass of the Earth

R = the distance from the centre of the Earth to the object in orbit.

To keep the 1 kg mass in orbit at an altitude of 100 km, an orbital speed of 7.85 km/s is needed.

The extra energy needed to make an object travel fast enough to stay in orbit is more than 30 times as much as the energy needed to lift it to an altitude of 100 km.

This means that, even though it takes nearly a million joules of energy to lift a 1 kg mass to an altitude of 100 km, it takes over 30 million joules of extra energy to give it enough speed to stay in orbit around the Earth.

Rockets need to be big enough to carry enough fuel to provide all of the energy needed to reach the correct altitude and speed. Rockets that carry satellites into orbit need to be incredibly large.

    Published 27 March 2013