Measuring the distance and masses of planets is easy

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

26 October 2008

Most readers send in one or two questions (at most three), but Daniel Kungu has set a record of sorts: He sent seven and I will try to answer them. First he wants to know what determines the flying height of a plane.

There are many factors, some are operational and others are technical. The major technical ones are the speed of the aeroplane and the angle of the flaps on its wings. When the pilot wants to maintain a certain height, she adjusts the velocity and the angle of the flaps.

The correct combination of speed and angle depends on the total weight of the plane and the weather condition - especially wind. Wind subtracts or adds the air velocity along the surface of the wings depending on whether it is along or against the direction of flight, respectively.

Daniels second question is: “How do scientists measure distance & weight of a distant planet?” Before attempting to answer, I need to make a small but important correction; it’s not “weight”, but mass. Weight is the gravitational force felt by an object while mass is a measure of the quantity of matter in the object.

Now the distance to planet is determined through trigonometry – the geometry of triangles. If you set a telescope at a point X to view the planet and then move it to a new place Y and view again, you will notice a small change in the viewing angle.

Knowing the distance from X to Y and the change in the viewing angle, it is easy to calculate the distance to the planet (remember Sines, Cosines and Tangents?). This is called “triangulation”. The only tricky part is how to move a heavy telescope from one place to another.

Instead of moving one telescope, it is easier to build two at locations whose distance apart is known and then comparing the angles of viewing one planet. For very large distances especially to other stars, the triangulation is done using the movement of the earth around the Sun.

The mass of a planet is determined from the velocity around the Sun and application of Newton’s law of universal gravitation. This law gives the relationship of three quantities, namely; the force of gravity between two bodies, their masses and their distance apart.

The first step is to measure the mass of the Earth (using its know radius and the gravitational force on the surface); next this value is used in measuring the mass of the Sun (using the distance determined by triangulation); then, finally the mass of the Sun is combined with the distance of the planet (from the sun) to work out the mass of the planet.

That sounds like a daunting task but it easy when you bear in mind that there are “libraryfuls” of historical data. Remember, astronomy is the oldest empirical science.

Two questions down, five to go. I will find time to answer the others in a future article. For now: I wish to honour the 300,000 candidates seating this year’s KCSE exams. Each is taking six subjects and each subject is examined in two or three papers. That makes a total of about 4 million examination papers.

Thus my tribute also goes to the examinations body: Let’s not crucify them if we find mistakes in 1,000 papers – it’s only a 0.024 percent failure, i.e., 99.976 percent score. Surely, that is exceptional performance by any standards!