Welcome to practical physicsPracticle physics - practical activities designed for use in the classroom with 11 to 19 year olds
 

Sketching a satellite orbit and predicting its period

Demonstration

Using a scale drawing to predict the time for a satellite close to the Earth. The results can later be compared with mathematical calculations based on v2/R.

Apparatus and materials

Brown paper sheet about 1.5 m long, 15 to 20 cm wide - or a roll of long paper

Thin wire, strong, about 3.5 m

Large mass or hook to anchor one end of the wire on the floor or near it

Metre rule with cm and mm markings

Health & Safety and Technical notes


Be careful with the thin wire, and avoid getting cuts to the hand.

This works best on the floor, or the side bench of a laboratory, with small groups of students. 
 
The arc drawn is twice as long as needed for 2 minutes' travel, but the double length enables a symmetrical drawing which will yield a good estimate more easily.

 

Procedure


a Using a thin wire anchored on the floor at one end and held taut with a pencil at the other end, draw an arc about 1.3 m long and with a radius of 3.3 m. The centre of the circle is not on the paper but arrange the paper so that the arc is. This represents part of a circular orbit for a satellite at an altitude of 200 km. (A scale drawing with 0.5 mm = 1 km - see Teaching Notes.)

Orbit of satellite

Sketch orbit to scale

b On that arc, XAY, mark the mid point A and part of the radius to A. Drop down along that radius the calculated fall 72 km (to scale) AM. (On the same scale 0.5 x 72 = 36 mm.) 
 
c Draw the tangent at A, symmetry helping. And draw a chord XMY parallel to the tangent, with mid point at M. 
 
d Transfer the fall AM out to the place where it should be shown as a fall from the tangent to the orbit, a fall NY. Measure the travel distance AY, which is covered in their chosen time 120 seconds (973 km). 
 
e Calculate the time for a complete orbit, knowing the total travel distance 2πR, which is 2π x 6,600 metres.


Teaching notes


1 A scale of 0.5 mm to 1 km is best for the drawing - a smaller drawing would be difficult to measure. On this scale, R = 6,400 + 200 km is represented by a radius of 0.5 x 6,600 = 3,300 mm = 3.3 m. 

2 Assume the satellite is always falling inward with acceleration g (≈ 10 m/s/s). First calculate how far the satellite will fall from the tangent in 1 second (5 m). It is clearly difficult to draw a scale diagram with 5 m drawn on it and the radius of the orbit, 6,600 km, and so a longer time needs to be chosen. the satellite's free fall from the tangent to its orbit in a time of 120 seconds will be s = 1/2 gt2 = 72 km. 
 
This will give a travel distance AY of about 973 km. The time for a complete orbit, T, will then be 120/T=973 / 2π x 6,600, giving a value of T of about 85 minutes. Students are generally very surprised to find that near-Earth satellites orbit with such short periods. Such satellites are used for astronomy, earth-observation (mapping and spying) and weather-forecasting. (Note that communications satellites must remain geostationary, and so orbit at much greater distances from the Earth.) 
 
It helps to provide illustrative date about a variety of near-Earth satellites. For example, the first artificial satellite, Sputnik 1, had an orbit period of 96.2 minutes. NASA has a website that offers real-time tracking of satellites, including the Hubble Space Telescope and the International Space Station. Likewise the European Space Agency has a satellites in orbit webpage, where you can find orbit information for its Earth Observation missions. [Note that ESA Space Science missions do not have near-earth orbits.] 

3 You could go on to calculate the Moon's orbital time, using the same scale. See the guidance note Estimating the Moon's orbit time

 

Related guidance


Estimating the Moon's orbit time

 

Weblinks


NASA

European Space Agency