Question

The U.S.S. Enterprise (NCC‑1701) approaches an unknown system with
a Black Hole at the center. One of the planets in this system is
observed to have an orbit with a radius of R_{1} = 2.6 AU
and a period of T_{1} = 0.4 years. What is the mass of the
Black Hole compared to the mass of the Sun?

The mass 109.81 solar mass

Another planet in the system is observed to have an
orbital radius of R_{2} = 6.6 AU, how long does it take for
this planet to complete one orbit around the Black Hole?

Answer #1

**part A)
given
R1 = 2.6 AU = 2.6*1.496*10^11 m
T1 = 0.4 years = 0.4*365*24*60*60 s
a) Let M is the mass of the block Hole**

**we know, T1 = 2*pi*R1^(3/2)/sqrt(G*M)**

**T1^2 = 4*pi^2*R1^3/(G*M)**

**M = 4*pi^2*R1^3/(G*T1^2)**

**=
4*pi^2*(2.6*1.496*10^11)^3/(6.67*10^-11*(0.4*365*24*60*60)^2)**

**= 2.189*10^32 kg**

**= 2.189*10^32/(1.99*10^30)**

**= 110*M_sun
<<<<<<<----------------Answer**

**part B)
we know,**

**According to Kepler's third law**

**square of the time period is proportional to cube of the
semi major axis of the planet.**

**T^2 is proportional to R^3**

**so, (T2/T1)^2 = (R2/R1)^3**

**T2/T1 = (R2/R1)^(3/2)**

**T2 = T1*(R2/R1)^(3/2)**

**= 0.4*(6.6/2.6)^(3/2)**

**= 1.62 years
<<<<<<<<----------------Answer**

We know that most of the mass (>99%) of the solar
system is in the Sun. Is this consistent with the masses you
calculated in the first table, and the solar system rotation curve?
Explain your answer.
Planet
Distance from Sun (AU)
Orbital Velocity (km/s)
Mass inside orbit = v2r/887
(solar masses)
Mercury
0.4
47.4
1.013195
Venus
0.7
35.0
0.966741
Earth
1.0
29.8
1.001172
Mars
1.5
24.1
0.982204
Jupiter
5.2
13.1
1.006056
Saturn
9.6
9.7
1.018335
Uranus
19.2
6.8
1.000910...

In January 2015, Caltech astronomers Konstantin Batygin and Mike
Brown proposed that a planet with about 10 times the mass of Earth
may exist in an orbit very far from the Sun.What is the orbital
period of this planet if it is on average 600 AU from the Sun?
(Use Kepler’s 3rd Law.). What if instead of the planet being a
“super” Earth roughly the size of Uranus or Nep- tune, it was not a
planet at all, but a...

The stars, gas and dust in a galaxy rotate about the center of
the galaxy. We would like to know exactly how to describe the
rotation of all parts of the galaxy. In other words, we want to
know if galaxies rotate like merry-go-rounds, or like planets orbit
the Sun, or in some other way.
1. Do points near the center of a merry-go-round complete a full
rotation in the same amount of time as points near the outer edge...

Astronomers have observed a small, massive object at the center
of our Milky Way galaxy. A ring of material orbits this massive
object; the ring has a diameter of about 10 light years and an
orbital speed of about 110 km/s .
a) Determine the mass of the massive object at the center of the
Milky Way galaxy. Give your answer in kilograms.
b) Give your answer in solar masses (one solar mass is the mass
of the sun).
c)...

What is the center of mass of our solar system? For this
problem, we can make a first order approximation that the center of
mass of our solar system is roughly the center of mass between our
sun and the planet Jupiter (since Jupiter has more mass than all
the other planets.) Is the center of mass inside the sun? The
distance between the sun and Jupiter is 7.78 x 10^11m. The mass of
the sun is 1.99 x 10^30kg...

2. A black hole with a mass equal to 6 billion solar masses
(6×109 Msun) lies at the center of the galaxy M87.
a. Calculate the Schwarzschild radius of this supermassive black
hole. Express your answer in kilometers (km), where 1 km = 1000 m.
(1 point)
b. Compare this Schwarzshild radius with the semi-major axis of
Neptune’s orbit, 4.5×109 km. (That is, divide one by the other to
determine the ratio.) Is the black hole, as defined by its...

Astronomers have observed a small, massive object at the center
of our Milky Way galaxy. A ring of material orbits this massive
object; the ring has a diameter of about 15 light years and an
orbital speed of about 140 km/s .
A: Determine the mass of the massive object at the center of the
Milky Way galaxy. Give your answer in kilograms.
B: Give your answer in solar masses (one solar mass is the mass
of the sun).
C:...

1.How did astronomers predict the existence of Neptune before
observing it?
Using astrological star charts
Looking at how its gravity affected Uranus's orbit
Following a mathematical pattern
Observing gaps in the Kuiper Belt
2.Ceres is a large, spherical body that orbits between Mars and
Jupiter. Why isn't it considered a planet?
It originated from outside the solar system
It was discovered with a telescope rather than observed by
ancient humans
It shares its orbital area with many other similarly sized...

Mark Watney, of The Martian fame, has somehow gotten himself
stuck on another, this time unknown, planet. You need to help him
perform some calculations so that he can, once again, escape the
planet’s surface and return to Earth. Here’s what Mark knows: ▪ He
has a mass of 77.5 kg and has found a capsule to launch in that has
a mass of 2542 kg. ▪ He is definitely still in our solar system. ▪
On the surface, he...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 3 minutes ago

asked 13 minutes ago

asked 28 minutes ago

asked 35 minutes ago

asked 41 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