How can Mars be colonized when it doesn’t have a magnetosphere?

Exactly the disappointing truth. It can’t. Since Mars is too small, the core cooled down long ago and therefore the organized magnetosphere doesn’t exist. Put as much atmosphere you want and it will still be blown away and not protect us from dangerous rays from the sun. We can only “colonize” the same way we “colonized” the Moon or the International Space Station: staying indoors!

Mars outpost near mesa
This image suggests how such a martian “motor home” might be realized. Providing transportation and housing for a crew of two to four human explorers, this pressurized rover would offer stability, visibility, storage, and a means for generating power for locomotion and electrical systems. A pair of wing-like solar arrays atop the rover help to meet some of the energy needs, and the transparent windshield ports have been coated to shield the interior from ultraviolet light and provide additional visual contrast to Mars’ rust-colored landscape.

Why do you believe we live on an oblate spheroid rotating over 1,000 mph that is spinning around the sun over 514,000 mph?

Earth is not a Harlem Globetrotter basketball spinning around on a finger.

The simple answer to your question why I believe is because this is what all the evidence has shown.

The word you use – spinning – is designed to indicate the earth is like a spinning top whizzing around and around at high speed. This is not true of Earth. Earth is rotating very slowly. Imagine a soccer ball on a table that turns around once every 24 hours. You could stare at it for a long time and not notice it move. The earth rotates half the speed of the hour hand on a clock. Can you see a clock’s hour hand move? It’s moving twice as fast as the earth is rotating.

So no. The earth is not spinning. It’s rotating very slowly. So slowly that there’s only a barely measurable difference in your weight at the equator than at the poles.

When we say it “spins” at just over 1000 mph at the equator it misleads some people to think that is so fast that things should go flying off into space. Think of it in terms of revolutions per minute (rpm).

Circular saw blades have an rpm of 3,000 to 50,000. Things fly off them. Cars sometimes have RPM gauges that measure RPM in the thousands. In the image below, this car redlines when the engine has an RPM of 7,000.

The rpm of Earth is 0.000694 RPM or about about 1/2 of one thousandths of an RPM.

Things don’t fly off something going just over 1/2 of one thousandths of an RPM. On the gauge below that would register as zero.