Ask question

Ask question

All categories

4 years ago

15

You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.

8×(10^7) m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 2.2×(10^11) m from its star with a period of 432 earth days. Once on the surface you find that the free-fall acceleration is 12.2 m/s^2.What is the mass of (a) the planet and (b) the star?

1 answer:

Novay_Z [31]4 years ago

5 0

Answer:

Mp= 1.48×10^23 Kg and M = 4.47×10^30 Kg

Explanation:

Given that

Diameter of planet D = 1.8×10^6m

Radius of planet Rp = 0.9×10^6m

Period of rotation of planet = 22.3 hrs = 80280s

Radius of orbit r = 2.2 × 10^11 m

Period of revolution around star T =432days = 432×24×60×60 = 37324800s

Acceleration of gravity on the surface of planet gp = 12.2m/s^2

gp = GMp/(Rp)^2

Mp = gp×(Rp)^2 /G

= 12.2 * (0.9*10^6)^2 ÷ 6.67×10^-11

9.882×10^12 ÷ 6.67×10^-11

Mp= 1.4×10^23 Kg

To determine the mass of the star, we consider the revolution of the planet around the star with period T

T^2 = (4π^2/GM)r^3

M = 4π^2r^3 ÷ GT^2

M = 4π^2* (2.2×10^11)^3 ÷ 6.67×10^-11 × ( 37324800)^2

M= 4.47×10^30 Kg

You might be interested in

Helen [10]

Answer:

15 protons and 18 electrons

General Formulas and Concepts:

<u>Chemistry</u>

Reading a Periodic Table
Element Number
Neutral Atoms
Ions

Explanation:

We are given the element P. P is 15 on the Periodic Table, meaning it has 15 protons and 15 electrons (all elements are in neutral form).

P³⁻ ion means the element now has a negative charge of 3. We know protons have a positive charge and electrons have a negative charge. 3- means we will have more electrons than protons.

Therefore, P³⁻ would have 15 protons and <em>18</em> electrons:

15 (+) + 18 (-) = 3 (-)

7 0

3 years ago

Read 2 more answers

A suspicious-looking man runs as fast as he can along a moving sidewalk from one end to the other, taking 2.20 s. Then security

Brilliant_brown [7]

Answer: The ratio is 1.54

Explanation:

Firs, we have to find the relative speed of the man moving forward and backward.

Forward:

vf = vs + vm

vm = the man's speed

vs = the sidewalk's speed

vf = relative velocity moving forward

Because we don't know how much the man moved,

vf = distance (meters) / time (seconds)

vf = x / 2.20s

Backward:

vb = -vm + vs

vb = relative velocity moving backward

vf = distance (meters) / time (seconds)

vf = -x / 10.30s

We now divide the relative speeds

vf / vb = (x / 2.20) / (-x / 10.30)

We cancel the x

vf / vb = -10.3s / 2.2s = -4.68

vf = -4.68 . vb

We now substitute this in the equation we used for the forward travel

-4.68vb = vm + vs

Subtracting this from the backward travel equation

vb - (-4.68vb) = -vm - vm + vs -vs

5.68vb = -2vm

vb = -2vm / 5.68

Now, adding to the backward travel equation

vb + (-4.68vb) = -vm + vm + vs + vs

-3.68vb = 2vs

Using the two resulting equations

-3.68 . (-2 / 5.68) vm = 2vs

7.36 / 5.68 vm = 2vs

vm / vs = 1.54

7 0

3 years ago

"a grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s. the angular speed is then increased to 1

kotegsom [21]

The average angular speed of the grindstone is 10 rad/s

$\texttt{ }$

<h3>Further explanation</h3>

<em>Let's recall </em><em>Angular Speed</em><em> formula as follows:</em>

$\boxed{ \omega = \omega_o + \alpha t }$

$\boxed{ \theta = \omega_o t + \frac{1}{2} \alpha t^2 }$

$\boxed{ \omega^2 = \omega_o^2 + 2 \alpha \theta }$

$\boxed{ \theta = \frac{( \omega + \omega_o )}{2} t }$

<em>where :</em>

<em>ω = final angular speed ( rad/s )</em>

<em>ω₀ = initial angular speed ( rad/s )</em>

<em>α = angular acceleration ( rad/s² )</em>

<em>t = elapsed time ( s )</em>

<em>θ = angular displacement ( rad )</em>

$\texttt{ }$

<u>Given:</u>

radius of the grindstone = R = 4.0 m

initial angular speed = ω₀ = 8.0 rad/s

final angular speed = ω = 12 rad/s

elapsed time = t = 4.0 seconds

<u>Asked:</u>

average angular speed = ?

<u>Solution:</u>

<em>Firstly , we will calculate </em><em>angular displacement </em><em>as follows:</em>

$\theta = \frac{( \omega + \omega_o )}{2} t$

$\theta = \frac{ ( 12 + 8.0 ) }{2} \times 4.0$

$\theta = 10 \times 4.0$

$\boxed {\theta = 40 \texttt{ rad}}$

$\texttt{ }$

<em>Next , we could calculate the </em><em>average angular speed</em><em> as follows:</em>

$\texttt{average angular speed} = \theta \div t$

$\texttt{average angular speed} = 40 \div 4.0$

$\boxed{\texttt{average angular speed} = 10 \texttt{ rad/s}}$

$\texttt{ }$

<h3>Learn more</h3>

Impacts of Gravity : brainly.com/question/5330244
Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
The Acceleration Due To Gravity : brainly.com/question/4189441
Moment of Inertia : brainly.com/question/13796477
The Ratio of the Moments of Inertia : brainly.com/question/2176655

$\texttt{ }$

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Rotational Dynamics

4 0

4 years ago

Read 2 more answers

In a group of Channel catfish, some individuals have a brown body and others have a white

alexandr402 [8]

Answer:

Bb

Explanation:

If the fish is brown, it had the dominant genotype.

8 0

2 years ago

Please help me with these I might need more than only 1 person to answer

Sindrei [870]

Explanation:

a) copper

b) olive oil

Hope it helps✌✌

7 0

3 years ago