If astronomers discovered a new planet and found its period of rotation around the Sun to be 105 years, how long would its semi-major axis length be as it orbited the Sun in AU?

If Astronomers Discovered A New Planet And Found Its Period Of Rotation Around The Sun To Be 105 Years,

Answers

Answer 1

From Kepler's third law, its semi-major axis length will be 22.2 AU approximately as it orbited the Sun in AU. The closest option is option C

Given that an astronomers discovered a new planet and found its period of rotation around the Sun to be 105 years.

According to Kepler's third law,

[tex]T^{2} \alpha r^{3}[/tex]

Where

T = Period ( in earth years) = time to complete one orbit

r = Length of the semi major axis in Astronomical unit.

[tex]T^{2}[/tex] = [tex]\frac{4\pi ^{2} }{GM} * r^{3}[/tex]

convert years to seconds

105 x 365 day x 24 hours x 3600 s

T = 3311280000 seconds

Mass of the sun M = 1.989 × 10^30 kg

G = 6.67 x [tex]10^{-11}[/tex]N m^2/kg^2

Substitute all the parameters into the formula

[tex]T^{2}[/tex] = 1.096 x [tex]10^{19}[/tex] = [tex]\frac{4\pi ^{2} }{6.67 * 10^{-11} * 1.989 * 10^{30} } * r^{3}[/tex]

1.096 x [tex]10^{19}[/tex] = 2.976 x [tex]10^{-19}[/tex] [tex]r^{3}[/tex]

[tex]r^{3}[/tex] = 1.096 x [tex]10^{19}[/tex] / 2.976 x [tex]10^{-19}[/tex]

[tex]r^{3}[/tex] = 3.68 x [tex]10^{37}[/tex]

r = [tex]\sqrt[3]{3.68 * 10^{37} }[/tex]

r = 3.33 x [tex]10^{12}[/tex] m

1 AU = 1.5 x [tex]10^{11}[/tex] m

r = 3.33 x [tex]10^{12}[/tex] / 1.5 x [tex]10^{11}[/tex]

r = 22.18 AU

Therefore, its semi-major axis length will be 22.2 AU approximately as it orbited the Sun in AU. The closest option is option C

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Answer 2

Answer:

C. 22.3 AU

Explanation:

Not only is the above an unnecessarily complicated answer, it's not even fully correct, and definitely not what they want you to do.

T^2 = s^3, where T = orbital period and s = semi-major axis length.

Substitute T and you get 105^2 = s^3. Solve for s.

11025 = s^3

3√11025 = s

22.25663649 = s

Therefore, the answer is C. 22.3 AU


Related Questions

What is the magnitude of the resultant of
a 3.0-
meter displacement and a 4.0-meter
displacement as shown in the diagram?
A. 1.0 meter
4.0 meters
B. 5.0 meters
3.0 meters
C. 7.0 meters
D. 12 meters

Answers

Answer:b. 5.0 meters

Explanation: d² = 3²+4²

d² = 9+16

d² = 25

d = √25

d = 5m

The magnitude of the displacement is 5 m as shown in the diagram. Option B is correct.

What is displacement?

Displacement can be defined as the total change in the position of the object. It is a vector quantity.

From the Pythagorean theorem,

[tex]d =\sqrt { 3^2 +4^2}\\\\d = \sqrt {25}\\\\d = 5[/tex]

Therefore, the magnitude of the displacement is 5 m.

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hlo anyone help
a stone is thrown upward with the kinetic energy of 10 joule if it goes up to a maximum height of 5 M find the initial velocity and mass of the stone??
Ty no spam plz help rn

Answers

Explanation:

Here, kinetic energy of the body, K.E=10 J

Height attained by the body, h=5 m

h=5m

When the body attains maximum height, its kinetic energy is converted into potential energy.

P.E=K.E

⟹mgh=10

⟹m= 10/gh

= m = 10/(10×5) =0.2 kg (taking the value g as 10m/s²)

Now, ½mv²=10

0.2×v²=20

v²=20/0.2

v²=100

v=√100

v=10m/s.

hope this helps you.

[tex]\huge \bf༆ Answer ༄[/tex]

Let's solve ~

As we know the total energy [P.E + K.E = C] of the system remains constant throughout the motion,

So, When a stone was thrown initially it didn't had any potential energy (P.E = 0) but had kinetic Energy of 10 joules.

So, total energy = P.E + K.E = 0 + 10 = 10 joules

As per the given information, equate it with the formula.

[tex] \sf \dfrac{1}{2}m {v}^{2} = 10[/tex]

[tex] \sf m {v}^{2} = 20[/tex]

Now, As it approaches 5m height it comes to rest, Therefore velocity = 0. And since velocity = 0 then Kinetic Energy = 0

Now, let's find the Potential Energy at that point ~

[tex] \sf mgh[/tex]

[tex] \sf m \times 10 \times 5[/tex]

[tex] \sf50m[/tex]

And here, the Total energy = P.E + K.E = 10 Joules

So,

[tex] \sf50m + 0 = 10 [/tex]

[tex] \sf50m = 10[/tex]

[tex] \sf m = 10 \div 50[/tex]

[tex] \sf m = 0.2[/tex]

Therefore, mass of the object is 0.2 kg = 200 grams

Now, plug the value of mass (m) in the equation of kinetic Energy to find the initial velocity of the stone ~

[tex] \sf m {v}^{2} = 20[/tex]

[tex] \sf0.2 \times {v}^{2} = 20[/tex]

[tex] \sf {v}^{2} = 20 \div 0.2[/tex]

[tex] \sf v = \sqrt{100} [/tex]

[tex] \sf v = 10 \: \: ms {}^{ - 1} [/tex]

Hence, velocity of the particle at the beginning was 10 m/s

Which is an action that can cause an object to move or change its state of motion? energy force equilibrium inertia

Answers

Answer:

correct

Explanation:

In physics, a force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Secondly, what force is necessary to change an object's motion?

Answer:

force

Explanation:

got it right on the test

What are inert gases with example ​

Answers

Answer:

Inert gases:An inert gas is a gas that is unreactive in its environment. The noble gases (helium, neon, argon, krypton, xenon, and radon) are considered inert in most applications. Argon is the cheapest noble gas and thus the most frequently used. In applications insensitive to chemical reactions with nitrogen, even nitrogen gas (N2) may be used as inert gas.
The noble gases make up a class of chemical elements with similar properties; under standard conditions, they are all odorless, colorless, monatomic gases with very low chemical reactivity. The six naturally occurring noble gases are helium, neon, argon, krypton, xenon, and the radioactive radon

explain how the spray painting process makes use of static electricity

Answers

Answer:

The spray paint gun is charged positively, which causes every paint particle to become positively charged. Since the paint particles all have the same charge, they repel each other and produce a fine mist of paint which is sprayed towards the wall/car.

Answer:

xerography can i get brainliest

Explanation:

An external force of 25 N acts on a system for 10 s. What is the impulse delivered to the system?

Answers

Answer:

I = 250N*s

Explanation:

I = F*t

I =  impulse or momentum

F = Force

t = time

I = 25N*10s

I = 250N*s

electromagnetic radiation at its maximum wavelength is:

Answers

Answer:

the radio wave. - The frequency ranges between 300 gigahertz (GHz) to 30 hertz (Hz).

Explanation:

what two properties change when light is refracted

Answers

Answer:

Refraction is merely one of several possible boundary behaviors by which a light wave could behave when it encounters a new medium or an obstacle in its path. The transmission of light across a boundary between two media is accompanied by a change in both the speed and wavelength of the wave.

Explanation:

What is the surface temperature of Sirius B in Kelvins?

Answers

Answer: The surface temperature of Sirius B is 25,200 Kelvins(K).

Explanation: You would think Sirius would have a surface temperature of 9,940 Fahrenheit. That is somewhat correct, but Sirius is a binary star consisting of a main-sequence star of spectral type A0 or A1, termed Sirius A, and a faint white dwarf companion of spectral type DA2, termed Sirius B. Sirius, Sirius A, and Sirius B, are all different stars. Sirius A has a temperature of 9,940 Kelvins, but Sirius B has a temperature of 25,200 Kelvins(K).

That would be 9,940 kelvins (K)

Hope it helps! :D

A battery is connected in series with an ammeter and a variable resistor R.
When R= 6.0 ohms, the current in the ammeter is 1.0 A. When R= 3.0 ohms, the current is 1.5 A.
Calculate the internal resistance of the battery.

A. 6.0 ohms
B. 1.5 ohms
C. 4.5 ohms
D. 3.0 ohms

Answers

The answer would be C

An object, initially at rest, moves 475 m in 19 s. What is its acceleration? *

Answers

u=0s=475mt=19s

[tex]\\ \sf\Rrightarrow s=ut+\dfrac{1}{2}at^2[/tex]

[tex]\\ \sf\Rrightarrow s=0(19)+\dfrac{1}{2}a(19)^2[/tex]

[tex]\\ \sf\Rrightarrow 475=\dfrac{361a}{2}[/tex]

[tex]\\ \sf\Rrightarrow 950=361a[/tex]

[tex]\\ \sf\Rrightarrow a\approx 2.3m/s^2[/tex]

If a category 6 hurricane would exist how fast do you think it would be?

Answers

My Answer:The scale starts with a Category 1, which ranges from 74 to 95 mph (119 to 153 km/h). A Category 5 storm has winds of 156 mph (251 km/h) or stronger. An extrapolation of the scale suggests that if a Category 6 were created, it would be in the range of 176-196 mph.

After the series of powerful storm systems of the 2005 Atlantic hurricane season, as well as after Hurricane Patricia, a few newspaper columnists and scientists brought up the suggestion of introducing Category 6, and they have suggested pegging Category 6 to storms with winds greater than 174 or 180 mph (78 or 80 m/s).

There is no such thing as a Category 6 hurricane. When Hurricane Irma was headed toward the coast of southern Florida in August, it had maximum wind speeds of 185 mph, according to the New York Times. But the Saffir-Simpson scale only goes up to 5.Hope it helps(◠ᴥ◕ʋ)

An object accelerates 2 m/s2 when an unknown force of 20 N is applied to it. What was the mass of the object?

Answers

Answer:

10 kg

Explanation:

The mass of an object given only the force acting on it and it's acceleration can be found by using the formula

[tex]m = \frac{f}{a} \\ [/tex]

f is the force in N

a is the acceleration in m/s²

We have

[tex]m = \frac{20}{2} = 10 \\ [/tex]

We have the final answer as

10 kg

Hope this helps you

What evidence is there that work is being done?
a) A lever is being used.
b) A simple machine makes a task easier.
c) The rock has a larger force than the boy.
d) The boy uses force to move the rock a distance.

Answers

Answer:

The boy uses force to move the rock a distance.

in the bohr model, what is the ratio of its kinetic energy to its potential energy?

Answers

The centrifugal force C = mv^2/r = kq^2/r^2 = P centripetal force. m is the electron mass, q are the proton and electron charges (opposites), and r is the Bohr radius.

Thus 1/2 mv^2/r = 1/2 kq^2/r^2 and KE = 1/2 mv^2 = 1/2 kq^2/r = 1/2 PE

Therefore KE/PE = 1/2, no matter what state the electron is in.

What is the acceleration of an object if it starts at a speed of 3 m/s and increases to
8 m/s in 20 seconds?

Answers

Answer:

0.25 meters per second squared

Explanation:


A woman of mass 49 kg jumps off the bow
of a 78 kg canoe that is intially at rest.
If her velocity is 4.5 m/s to the right, what
is the velocity of the canoe after she jumps?
Answer in units of m/s i.
x x

Answers

The woman-canoe system has zero initial momentum. When the woman jumps from the canoe, the total momenta of the woman and canoe is conserved, so that

0 = (49 kg) (4.5 m/s) + (78 kg) v

where v is the velocity of the canoe. Solving for v, we find

(78 kg) v = - (49 kg) (4.5 m/s)

v = - 49/78 (4.5 m/s)

v ≈ -2.8 m/s

which is to say, the boat is given a velocity of 2.8 m/s to the left.

a -0.06 C charge is placed in a uniform electric field with a strength of 200 N/C. what is the magnitude and direction of the force on the charge​

Answers

The  magnitude and direction of the force on the charge​ is -12 N opposite the electric field

To calculate the force on a charge in an electric field, we make use of the formula below.

Formula

F = E×Q .......................... Equation 1

Where:

F = Force on the chargeE = Electric FieldQ = charge

From the question,

Given:

E = 200 N/CQ = -0.06 C

Substitute these values into equation 1

F = 200(-0.06)F = -12 N

Note: The negative sign indicates that the force is in the direction negative of the electric field.

Hence, The  magnitude and direction of the force on the charge​ is -12 N opposite the electric field

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Answer: A edge 202694020

Explanation:

Jeff Gordon leads his race and must drive into a curve at top speed to win it all. The radius of the curve is 1000 m and the coefficient of static friction between his tires and the dry pavement is 0.50.

Answers

Answer:

Apparently the curve is not banked.

The maximum frictional force is -

Ff = m g * .5

Fc = m v^2 / R     where Fc is the centripetal force that must be present in

                            order for the car not to slip.

.5 g = v^2 / R      equating forces

v^2 = .5 R g = .5 ^ 1000 * 9.80

v = (500 * 9.80)^1/2 = 70 m/s

(about 230 ft/sec = 230/88 * 60 = 157 mph

A crane does 9,500 J of work to lift a crate straight up using a force of 125 N. How high does the crane lift the crate? 0. 013 m 76 m 9,400 m 1,200,000 m.

Answers

The distance covered as the crane does work is 76 m.

Recall that the work done in lifting the crane is the product of force and distance covered. In this case, we are talking about the distance through which the crane is raised. Therefore;

Work done = Fs

F = Force applied

s = Distance covered

Substituting values;

Work done/Force applied = Distance covered

Distance covered = 9,500 J/125 N

Distance covered = 76 m

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A neutral object has:

a. Zero electrons.
b. Zero protons.
c. Only neutrons.
d. An attraction to negative objects.
e. An attraction to neutral objects.

Answers

Answer:

c. Only neutrons.

hope it helps :)

which term is equal to velocity change per second?

Answers

Answer:

Acceleration  is measured in meters per second squared (m/s²) change in velocity is measured in meters per second (m/s) time taken

astronomers have determined the surface temperature of stars by studying their colors. what color emission represents stars with the hottest temperatures?

Answers

Answer:

Blue

Explanation:

Did the question already

The table below describes some features of methods used to generate electricity. What is method 3?

Answers

Answer:

dam/hydro power

Explanation:

estuary is the place where rivers meet the ocean, there are a lot of currents there (waves...) so it likely means thery use a dam or some sort of way of collecting electricity from the motion of the water there. many birds live in estuaries because of being able to find fish to feed from

Method 3 is "Estuary." describes some features of methods used to generate electricity.

An estuary is a coastal area where freshwater from rivers meets and mixes with saltwater from the ocean. This mixing creates a unique and dynamic environment that can be harnessed for electricity generation using a method called "tidal energy" or "tidal power." Tidal energy is a renewable energy source that captures the kinetic energy generated by the ebb and flow of tides in estuaries.

Ideal Location: Estuaries are ideal locations for tidal energy generation because they experience regular and predictable tidal movements due to the gravitational pull of the moon and sun. The rise and fall of tides create kinetic energy in the moving water.

Method: Tidal energy is harnessed using underwater turbines that are placed in strategic locations within the estuary. As the tidal currents flow in and out, they drive the turbines, which generate mechanical energy. This mechanical energy is then converted into electricity using generators.

Possible Problem: One potential problem associated with tidal energy generation in estuaries is its impact on the local ecosystem. The underwater turbines and infrastructure could potentially disrupt marine life and habitats, affecting fish migration patterns and other aquatic species. It's important to carefully study and manage the environmental impact of tidal energy projects to minimize any negative consequences.

Overall, tidal energy from estuaries offers a renewable and predictable source of electricity, but it requires careful planning and environmental considerations to ensure sustainable and responsible energy production.

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Question 4 of 10
When you go along with a group because you don't want to cause trouble, it is
called:
A. informational social influence.
B. normative social influence.
C. attribution
.
D. fundamental social influence.

Answers

Answer:

Normative

Explanation:

It is normal occurance but not unnatural

What is the density of a substance that has a volume of 30ml and a mass of 20g?

Answers

Answer:

0.67 g/mL

Explanation:

The density of a substance can be found by using the formula

[tex]d = \frac{m}{v} \\ [/tex]

m is the mass

v is the volume

From the question

m = 20 g

v = 30 mL

We have

[tex]d = \frac{20}{30} = \frac{2}{3} \\ = 0.66666...[/tex]

We have the final answer as

0.67 g/mL

Hope this helps you

Convert 8 m/s to miles per hour

Answers

Answer:

17.8954903 or 17.9 mph

Explanation:

m/s is meters per second. 1609.344 meters is one mile. There are 3,600 seconds in an hour.  8 meters *3600 seconds= 28,800.  28,800/1609.344 = 17.8954903. Simplify to 17.9


A mass is pulled to the right while on a table.
A. Label the forces.
5 kg
B. Calculate the
object's weight.

Answers

Answer:

weight in 49N

I hope it's correct

I keep people warm I come in many different colors, styles, and materials. many people use me when they sit on a couch

Answers

Answer:

a seat

Explanation:

The phrase “seat value” is used in the hospitality and bar sectors to describe how much money each seat or square foot of customer area must generate to justify its existence.

What is the use of seat by the people?

An area to sit is a seat. The phrase may also refer to headquarters in a more general meaning as well as extra elements such a back, armrest, and head restraint.

Being in the centre allows you to benefit from both the advantages of both front and back seating while balancing out their extremes. While you're still close enough to be paying careful attention to the lecture, the middle rows will relieve you of the pressure and expectations of the front.

By remaining seated, students help avoid physical altercations. There is more time spent on task when pupils are seated.

Environmental psychology, which gives people the impression that they have some degree of influence over their daily lives, is the driving force behind all of this behavior.

Therefore, seat used by people.

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Approximately how many kilograms (kg) of carnivore (secondary consumer) biomass can be supported by an area of a field containing 1,000 kg of plant material (assuming 10% efficiency in energy transfer)

Answers

Only 10 Kg of secondary consumers can be supported by the ecosystem.

There exists such a thing as the 10% rule in the transfer of energy in biomass from one trophic level to another. This rule ultimately controls the mass of biomass that is available at the next higher trophic level.

This rule state that only 10% of the energy in biomass is transferred to the next trophic level. By this rule, only 10% of the energy in the plant material is transferred to the carnivore population. Therefore, only 10 Kg of secondary consumers can be supported by the ecosystem.

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