Geophysics of Tekuo : more hard sums

The planet’s size, mass and composition, and how they affect the locals.

Readers may recall that an earlier post, Tekuo, astronomy and hard sums, looked at the planet Tekuo and its place in the solar system of Ayu. This post looks more closely at the planet itself.

How big is Tekuo?

The planet, naturally, is a sphere. Geometry teaches us that once we know the radius of a sphere much else can be calculated from it. The earlier post noted only that the radius of Tekuo is 0.9 times the radius of Earth. Earth has a radius of 6,371 km. The radius of Tekuo is exactly 0.9 of this, i.e. 5,734 km.

For comparison, the radius of Venus is around 0.94 times the radius of Earth. The radius of Almea is around 0.84 times that of Earth and the radius of Mars is around 0.53 times that of Earth.

The diameter of a sphere diameter is twice its radius. The diameter of Earth is therefore 12,742 km and the diameter of Tekuo is 11,468 km, again, 0.9 of the diameter of Earth. Some of the planet’s other key measurements, though, are around 80% of the figure for Earth.

We can also now calculate  the circumference, using the formula:

2πr (2 x π x radius)

This tells us that the circumference of Tekuo is 36,027.8 km. By way of comparison, the circumference of Earth is 40,030 km.

From Tekuo’s radius, we can also calculate  its surface area, using the formula:

4πr² (4 x π x radius squared)

This formula tells us that the surface area of Earth is 510,072,000 km² (of which: 148,940,000 km² is land, 29% of the total, and 361,132,000 km² is water).

It also tells us that the surface area of Tekuo is 413,167,000 km² (of which: 99,160,080 km²2 is land, 24% of the total, and 314,006,920 km² is water). The land area of Tekuo is a little less than that of Africa, Eurasia and South America. They have a combined area of 102,800,532 km².


Weighty matters

From a planet’s radius, we can also calculate its volume and mass. These figures are not particularly interesting in themselves, but we need them in order to calculate some more interesting figures.

The volume of a sphere may be found with the formula:

4/3πr³ (4 thirds x π x radius cubed)

The volume of Earth is therefore 1.083 21 x 10¹² km³. The volume of Tekuo is 0.73 times that of Earth, i.e.  0.789 70 x 10¹² km³.

The mass of a sphere is its volume times its density. The density of Earth is 5.514 g/cm³ (grammes per cubic centimetre). Venus has a density of 5.2 g/cm³. The density of Tekuo lies between the two, at 5.4 g/cm³.

The mass of Tekuo is therefore 5.4 times 0.789 70 x 10¹² km³. This works out as 4.264 38 x 10 to the power 24 km³. This figure is 0.714 times the mass of Earth. Earth has a mass of 5.972 37 x 10 power 24 km³.


Some consequences

This new information is of little interest to creatures like us, living on the planet’s surface. With this information, though, we can now calculate the planet’s gravity and air pressure. These two factors are of great interest to us.

The gravity of a body is its mass over the square of its radius. Tekuo has a mass of 0.714 Earth’s and the square of its radius is 0.81. Its gravity is therefore 0.881 times that of Earth. The gravity of Earth is 9.807 metres/second. The gravity of Tekuo is, therefore, 8.63m/s.

Note that these figures represent rates of acceleration of an object under the effect of gravity. They are not measures of speed.

The difference between the gravity of Earth and the gravity of Tekuo is not always observable in everyday life. If a visitor from Earth dropped something on Tekuo, they would get a vague sense that something was not quite right in the way it fell. If they dropped something over a cliff though, it would clearly fall more slowly.

In contrast, the effect on horizontal movement would be much more noticeable. A ball rolled along the ground would travel further and faster due to Tekuo’s weaker gravity. If the ball were thrown instead, it would travel further before falling to the ground.

An Earth visitor’s subjective awareness of their own movements would be altered, too. Our muscles are designed for stronger gravity, so activity on Tekuo would seem easier and be much less tiring.

Gravity, in turn, affects air pressure, but it is not the only factor. The density of the atmosphere is also a factor. The density of the atmosphere depends on which gases are present in what quantities.

Earth has a surface air pressure 101.325 kPa (at mean sea level). Mars has 63.6 kPa and Venus has 92 kPa. The Earth figure may also be represented as 1 atmosphere (1 atm).

The atmosphere of Tekuo has a similar composition to that of Earth. However, it’s weaker gravity makes its air pressure lighter. Tekuo has a surface air pressure of around 83 kPa. This represents about 0.82 atm., i.e. about 0.82 times the surface air pressure of Earth.

A human visitor from Earth would find breathing on Tekuo was possible, but a struggle. They would be constantly gasping for air. They would experience dizziness and tiredness, despite the ease of movement mentioned above.

Over a short stay on Tekuo, it might be possible for them to get used to this. In the long-term, the cells in their body would suffer from the lack of oxidisation. It would be best to pack breathing equipment such as a CPAP machine. This would help the visitor to maximise their oxygen supply.


Miscellaneous

Tekuo has an axial tilt of 21°. This is comparable to the 23.5° tilt of Earth. It thus has a similar range of seasons in its weather.

Finally, we should note that the subtle and mysterious energy known in Lemohai as phao has a mean background level of 3.37 batã. We will look more closely at phao in a later post.

Author: David Johnson

Conlanger, writer and activist.

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