World of Science at AEASC

With so many past and present missions to sent to Mars, scientists understand Mars’ surface better than any other planet in the Solar System (other than Earth, of course).

Mars is actually quite a small world. It has a radius of less than half the Earth, and about one-tenth the mass. Its total surface area is about 28% the size of Earth. This doesn’t sound like much, but it’s actually almost exactly the same amount as the dry land on Earth. So there’s a lot room to explore on Mars.

The surface of Mars seems to be mostly basalt, covered by a fine layer of iron oxide dust that has the consistency of talcum powder. It’s this iron oxide dust that gives Mars its red color.

The planet has no surface liquid water, so it’s very similar to the driest deserts on Earth. If you could stand on the surface of Mars, you would see rocks and boulders strewn about in all directions, covered by this red dust.

There are some unique features on the surface of Mars, like the giant shield volcano, Olympus Mons, which towers 27 km above the surrounding plains. And there are three other shield volcanoes which are almost as large. And then there’s the enormous Valles Marineris trench, which cuts a 7 km deep scar across 4,000 km of the Martian equator.

There are many processes on Earth that wear away features over time: rain, wind and even plate tectonics. There’s nothing like that on Mars. This means that the Mars surface is dotted with craters large and small. Without a thick atmosphere, even small space rocks can impact the surface of the planet.

How seasonal jets darken the surface of Mars, and how ice depth varies across Mars.

Want to explore the surface of Mars, check it out with Google Mars. Here is some more information about surface features on Mars.

Finally, if you’d like to learn more about Mars in general, we have done several podcast episodes about the Red Planet at Astronomy Cast. Episode 52: Mars, and Episode 91: The Search for Water on Mars.

When we mentioned in the introduction that a vector is either an ordered pair or a triplet of numbers we implicitly defined vectors in terms of components.

Each entry in the 2-dimensional ordered pair (a, b) or 3-dimensional triplet (a, b, c) is called a component of the vector. Unless otherwise specified, it is normally understood that the entries correspond to the number of units the vector has in the x , y , and (for the 3D case) z directions of a plane or space. In other words, you can think of the components as simply the coordinates of the point associated with the vector. (In some sense, the vector is the point, although when we draw vectors we normally draw an arrow from the origin to the point.)

Figure %: The vector (a, b) in the Euclidean plane.

Vector Addition Using Components

Given two vectors u = (u 1, u 2) and v = (v 1, v 2) in the Euclidean plane, the sum is given by:

u + v = (u 1 + v 1, u 2 + v 2)

For three-dimensional vectors u = (u 1, u 2, u 3) and v = (v 1, v 2, v 3) , the formula is almost identical:

u + v = (u 1 + v 1, u 2 + v 2, u 3 + v 3)

In other words, vector addition is just like ordinary addition: component by component.

Notice that if you add together two 2-dimensional vectors you must get another 2-dimensional vector as your answer. Addition of 3-dimensional vectors will yield 3-dimensional answers. 2- and 3-dimensional vectors belong to different vector spaces and cannot be added. These same rules apply when we are dealing with scalar multiplication.
Scalar Multiplication of Vectors Using Components

Given a single vector v = (v 1, v 2) in the Euclidean plane, and a scalar a (which is a real number), the multiplication of the vector by the scalar is defined as:

av = (av 1, av 2)

Similarly, for a 3-dimensional vector v = (v 1, v 2, v 3) and a scalar a , the formula for scalar multiplication is:

av = (av 1, av 2, av 3)

So what we are doing when we multiply a vector by a scalar a is obtaining a new vector (of the same dimension) by multiplying each component of the original vector by a .
Unit Vectors

For 3-dimensional vectors, it is often customary to define unit vectors pointing in the x , y , and z directions. These vectors are usually denoted by the letters i , j , and k , respectively, and all have length 1 . Thus, i = (1, 0, 0) , j = (0, 1, 0) , and k = (0, 0, 1) . This enables us to write a vector as a sum in the following way:

(a, b, c) = a(1, 0, 0) + b(0, 1, 0) + c(0, 0, 1)
= a i + b j + c k

Vector Subtraction

Subtraction for vectors (as with ordinary numbers) is not a new operation. If you want to perform the vector subtraction u – v , you simply use the rules for vector addition and scalar multiplication: u – v = u + (- 1)v .

In the next section, we will see how these rules for addition and scalar multiplication of vectors can be understood in a geometric way. We will find, for instance, that vector addition can be done graphically (i.e. without even knowing the components of the vectors involved), and that scalar multiplication of a vector amounts to a change in the vector’s magnitude, but does not alter its direction.