1) The document discusses gravitational forces between planets and how they follow Kepler's laws, with closer planets moving faster around the sun. 2) It also describes comets and meteors, with comets composed of ice and rock that heat up close to the sun, and meteors being rocks that burn up entering a planet's atmosphere. 3) Finally, it talks about dark energy and dark matter, with dark energy being a property of space that causes it to expand, and dark matter being an unseen matter that accounts for 27% of the universe.

1. MATHEMATICS
IN THE UNIVERSE
Presented by:
Ralph Justine Alconaba, Lord Jervy Thomson Leopoldo,
Louise Angela Villanueva
MATHEMATICS IN THE MODERN WORLD

2. GRAVITATIONAL PULL AMONG
THE PLANETS

3. Gravity is dependent on
mass, where all things –
from stars, planets, and
galaxies to light and
sub-atomic particles –
are attracted to one
another.

4. Depending on the size, mass and
density of the object, the
gravitational force it exerts varies.

5. Gravitational pull of the
planets

6. COMETS AND METEORS

7. COMETS
• Comets are frozen leftovers from
the formation of the solar system
composed of dust, rock and ices. They
range from a few miles to tens of
miles wide, but as they orbit closer
to the sun, they heat up and spew
gases and dust into a glowing head
that can be larger than a planet.
This material forms a tail that
stretches millions of miles.

8. Comets go around the Sun in a
highly elliptical orbit. They can
spend hundreds and thousands of
years out in the depths of the solar
system before they return to Sun at
their perihelion. Like all orbiting
bodies, comets follow Kepler's
Laws - the closer they are to the
Sun, the faster they move.

9. HALLEY'S COMET

10. METEORS
• When meteoroids enter Earth’s
atmosphere (or that of another
planet, like Mars) at high speed
and burn up, the fireballs or
“shooting stars” are called
meteors.

11. A meteor shower occurs when Earth passes through this material, which
generally happens at only one point in its orbit. As Earth passes that point
at the same time every year, we can predict meteor shower times with good
accuracy.

12. DARK ENERGY AND
DARK MATTER

13. DARK ENERGY
One explanation for dark energy is
that it is a property of space. Albert
Einstein was the first person to
realize that empty space is not
nothing. Space has amazing
properties, many of which are just
beginning to be understood. The
first property that Einstein
discovered is that it is possible for
more space to come into existence.

14. DARK MATTER
First, it is dark, meaning that it is
not in the form of stars and planets
that we see. Observations show that
there is far too little visible matter
in the universe to make up the 27%
required by the observations. Second,
it is not in the form of dark clouds
of normal matter, matter made up of
particles called baryons.

15. • network like pattern
• If cold dark matter is in charge, those filaments quickly
fragment into clumps, causing the protogalaxies to
emerge as separated clusters of stars. Otherwise,
newborn stars light up entire filaments, with fuzzy
dark matter imprinting an additional interference-like
pattern on the arrangement.
• It shaped entire galaxies without touching a thing.

18. THANK YOU!

19. REFERENCES
• https://phys.org/news/2016-01-strong-gravity-planets.html
• https://solarsystem.nasa.gov/asteroids-comets-and-
meteors/comets/overview/?page=0&per_page=40&order=name+asc&s
earch=&condition_1=102%3Aparent_id&condition_2=comet%3Abody_t
ype%3Ailike
• https://www.st-
andrews.ac.uk/~bds2/ltsn/ljm/JAVA/COMETORB/COMET.HTM
• https://astronomy.com/magazine/ask-astro/2011/10/calculating-falling-
stars?fbclid=IwAR35Hi28GTBRVqNd-
RwYwa3BYKUhFVtaKeyObLMpWoOvVaH9FfiDAsUyFTI
• https://science.nasa.gov/astrophysics/focus-areas/what-is-darkenergy
• https://physics.aps.org/articles/v12/s112