Question

Kepler’s Laws of Planetary Motion:

1. A newly discovered exoplanetary system has a planet orbiting its host star at 50 times the distance from the Earth to the sun. If the orbital period of the planet is 40 Earth years, what is the mass of the host star?

2. The mass of the Earth is approximately 6 × 10^{26}
kg. If the moon takes 27 days to orbit the Earth, how far is the
moon from the Earth?

3. A satellite is placed into geosynchronous orbit around the Earth (That means that it orbits once per day and thus stays above the same location over the Earth). Compute the distance from the Earth that the satellite is at.

Answer #1

Using formula of time period, mass of host star can be calculated.

Kepler’s Laws of Planetary Motion:
1. A satellite is placed into geosynchronous orbit around the
Earth (That means that it orbits once per day and thus stays above
the same location over the Earth). Compute the distance from the
Earth that the satellite is at.

The planet Gliese 163 c, discovered in 2012, is a potentially
habitable world which is approxi- mately 7 times same mass as the
Earth, orbiting a small red dwarf star that is only 0.4 times mass
of the Sun. Completing its entire orbit in only a little over 25
days, Gliese 163 c orbits at a distance from its star at a speed of
1.78 times that of the speed of the Earth around the Sun.
Approximating that both the...

Planet Yoyo is discovered to orbit around a star with 5 times
the mass of our Sun. It orbits at a distance of 7 AU in a circular
orbit. The orbital period is measured to be 8 years. Find:
1) The mass of the planet. Give the answer in both solar masses
and kilograms
2) The mass of the star in kilograms
3) The distance of the planets orbit in meters.
4) The force due to gravity between the planet...

Could you find the Mass of the Sun using the slope of the of
T2 versus a3, using the values that are in
units of years and AU? Explain.
Suppose we discovered a planetary body orbiting our Sun at a
distance of 15 AU. How long would this world take to complete one
orbit around the Sun? (show your work)
Suppose Astronomers noticed a moon around the newly discovered
planet in Question 2. By watching this moon, noting its period...

7. Two satellites are moving
around Earth following orbits of the same radius. Satellite 1 has
mass equal to half of mass of satellite 2. We can conclude
that:
Speed of satellite 1 is twice as big as speed of satellite
2.
Speed of satellite 1 is half of speed of satellite 2.
Speed of satellite 1 is the same as speed of satellite 2.
Speed of satellite 1 in fours times speed of satellite 2.
Speed of satellite 1...

A new planet has been discovered. This planet has an
eccentricity of 0.664 and orbits a star of mass 8.72×10^30 kg with
a period of 5.72 years.
1. What is the semi-major axis of the planet's
orbit?
2. What is the average velocity of the planet in its
orbit?
3. What is the distance of closest approach to its
parent start (perihelion)?
4. What is the farthest distance the planet travels away
from its parent start (aphelion)?

A new extrasolar planet (outside our solar system) has been
discovered. This planet orbits a star of mass 1.05×1031 kg with a
period of 6.52 years . It is also known that the planet has an
eccentricity of 0.674.
Part A: What is the average velocity of the planet in its orbit?
in m/s
Part B: What is the distance of closest approach to its parent
start (perihelion)? d.perihelion in m
Part C: What is the farthest distance the planet...

Kepler 1606b is an exoplanet: a planet orbiting a star different
than our own. Named for the star it orbits (Kepler 1606, a star
about 3000 light-years away), it was discovered in the year 2016 by
the Kepler space telescope.
Kepler 1606b orbits its star a little bit closer than the
Earth's orbit to the Sun, at a distance of 0.64⋅rearth, where
rearth=1.50×1011 m is the radius of Earth's orbit. The star Kepler
1606 is bit cooler than our Sun,...

The planet Mercury has an orbital period of 87.97 days, and its
greatest distance (aphelion distance) from the Sun is 0.4667 AU
{where 1 AU " 1 Astronomical Unit = 1.496x1011 m}. The mass of the
planet Mercury is 3.302x1023 kg and the mass of the Sun is
1.988x1030 kg. (a) Calculate the eccentricity of planet Mercury’s
orbit around the Sun. ! (b) Calculate the highest speed of planet
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14. Consider an artificial Satellite whose PERIGEE (closest
point to Earth) is 3000 miles above the Earth’s surface and whose
APOGEE (farthest point to Earth) is 4200 miles above the surface.
If we compare the satellite with Moon’s that is 239,000 miles far
from the Earth and its time period is 27.3 days. Find the time
period of the Satellite?
Note: Radius of Earth is 3960 miles and average distance
is
R = (Rmax + Rmin) / 2
15. If...

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