Question

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 Earth’s orbit and Gliese 163 c’s orbit can be taken to be nearly circular, with gravity providing centripetal force, what must be its average orbital distance from its star compared with the Earth's average orbital distance to the Sun?

Answer #1

For Earth-Sun system, Gravity providing the centripetal force

---(1)

For planet Gliese and its red dwarf star,

Gravity providing the centripetal force

----(2)

Given that , Mass of Gliese is 7 times same mass as the Earth

Mass of red dwarf star that is only 0.4 times mass of the Sun

Speed of Gliese around red dwarf star is 1.78 times that of the speed of the Earth around the Sun ,

Average orbital distance from Gliese to Red dwarf star is times the average orbital distance from Earth to Sun.

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 × 1026
kg. If the moon takes 27 days to orbit the Earth, how far is the
moon from the Earth?
3. A...

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...

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...

The minimum distance of a comet from the Sun is observed to be
an eighth of the radius of the Earth’s orbit (which
is assumed to be circular), and its speed at that point (the
perihelion) is four times the orbital speed vE of the Earth.
The orbits of the Earth and comet are coplanar.
a) Find the comet’s speed in terms of vE when it crosses the
Earth’s orbit, and the angle at which the orbits cross.
b) Will...

a) Your cosmic journey brought you into the vicinity of a
neutron star. In fact, you are orbiting this neutron star at an
orbital distance of 2,184 kilometers. The neutron star has mass of
1.6 solar masses (MSun = 1.99 × 1030
kg).
What is the local acceleration due to gravity that you experience
in your spaceship? Express your answer in m/s2; use
scientific notation and round the coefficient to two decimals.
b) What is the escape velocity from Earth’s...

Astronomers are constantly discovering new planets orbiting
nearby stars. In the following scenario, compare the gravitational
force between the planet and its star to the gravitational force
between the Earth and the Sun and enter your result as a decimal
with no units. (For instance, if the gravitational force between
the planet and the star is 1/4 the gravitational force between the
Earth and the Sun, enter 0.250)
A planet that has a mass 7.93 times that of the Earth...

a) In 2017, NASA announced the discovery of seven planets with
sizes similar to the Earth orbiting a red dwarf star 40 light years
away. Based on the data in the table shown, what is the
acceleration due to gravity on planet g?
(B) Use the orbital data for planet g and Kepler's 3rd Law to
find the mass of the star these planets orbit. Give your answer
relative to the Sun's mass. For example, if the star were 1/2...

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⋅?????ℎ, where
?????ℎ=1.50×1011 m is the radius of Earth's orbit. The star Kepler
1606 is bit cooler than our Sun,...

9. Planet Berth! Imagine a planet, which we’ll call
Berth, orbiting a star identical to the sun at a distance of 1 AU.
Assume that Berth has eight times as much mass as Earth and is
twice as large as Earth in diameter.
a) How does Berth’s density compare to Earth’s
b) How does Berth’s surface area compare to the Earth’s?
c) Based on your answers to a) and b), discuss how Berth’s
geological history is likely to have differed...

A binary pulsar is a system of two neutron stars of equal mass
(each about 1.4 times the mass of the sun and a radius of 10km). A
particular binary pulsar has two neutron stars orbiting around
their center of mass, and separated by a (center to center)
distance of d= 7.0*10^8m. Assume the orbit is circular.
a) Calculate the orbital speed of the stars in meters/second.
b) Calculate the magnitude of the centripetal acceleration of one
of the stars...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 18 minutes ago

asked 29 minutes ago

asked 44 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago