1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Rzqust [24]
3 years ago
14

Every few hundred years most of the planets line up on the same side of the Sun.(Figure 1)Calculate the total force on the Earth

due to Venus, Jupiter, and Saturn, assuming all four planets are in a line, as shown in the figure. The masses are MV=0.815ME, MJ=318ME, MSat=95.1ME, and the mean distances of the four planets from the Sun are 108, 150, 778, and 1430 million km.

Physics
2 answers:
mylen [45]3 years ago
4 0

Answer: 3.7 \times 10^{-4} N

Explanation:

The gravitational pull between two object is given by:

F = G\frac{Mm}{r^2}

Where M and m are the masses of the object, r is the distance between the masses and G = 6.67× 10⁻¹¹ m³kg⁻¹ s⁻² is the gravitational constant.

We have to calculate the net force on Earth due to Venus, Jupiter and Saturn when they are in one line. It means when they are the closest distance.

F_{net] = G\frac{M_eM_v}{r_v^2}+G\frac{M_eM_j}{r_j^2}+G\frac{M_eM_s}{r_s^2}

Mass of Earth, Me = 5.98 × 10²⁴ kg

Mass of Venus, Mv = 0.815 Me

Mass of Jupiter, Mj = 318 Me

Mass of Saturn, Ms = 95.1 Me

closest distance between Earth and Venus, rv = 38 × 10⁶ km = 0.25 AU

closest distance between Jupiter and Earth, rj = 588 × 10⁶ km = 3.93 AU

closest distance between Earth and Saturn, rs = 1.2 × 10⁹ km = 8.0 AU

where 1 AU = 1.5 × 10¹¹ m

Inserting the values:

F_{net} = G\frac{M_e\times 0.815 M_e}{(0.25AU)^2}+G\frac{M_e\times 318 M_e}{(3.93AU)^2}+G\frac{M_e\times 95.1 M_e}{(8.0AU)^2}\\ \Rightarrow F_{net} = \frac{(GM_e^2)}{(1AU)^2}(\frac{0.815}{0.25^2}+\frac{318}{3.93^2}+\frac{95.1}{8.0^2})=\frac{6.67\times 10^{-11} \times (5.98\times 10^{24})^2}{(1.5\times 10^{11})^2}(35.1) = 3.7 \times 10^{-4} N

Dmitry [639]3 years ago
3 0

The net Gravitational force acting on the Earth \fbox{\begin\\9.559 \times {10^{17}}{\text{ N}}\end{minispace}}.

Further Explanation:

The net force acting on a body is the vector sum of all the forces acting on the body.

Given:

Venus mass is 0.815M_E.

Jupiter mass is 318 M_E.

Saturn mass is 95.1M_E.

Distance between Venus and Sun is 108\text{ million}\text{ km}.

Distance between Earth and Sun is 150\text{ million km}.

Distance between Jupiter and Sun is 778\text{ million km}.

Distance between Saturn and Sun is 1430\text{ million km}.

Concept:

The expression for the Gravitational force of attraction is:

F = \frac{{G{M_1}{M_2}}}{{{R^2}}}                                …… (1)

The value of the gravitational constant is 6.67 \times {10^{ - 11}}{\text{ }}\frac{{{\text{Nm}}}}{{{\text{k}}{{\text{g}}^2}}}.

The mass of the Earth is 5.97 \times {10^{24}}{\text{ kg}}.

The expression for the distance between the Earth from the Venus is:

{R_{{\text{EV}}}} = {R_{{\text{SE}}}} - {R_{{\text{SV}}}}

Substitute 108 for {R_{{\text{SV}}}} and 150 for {R_{{\text{SE}}}} in the above equation.

\begin{aligned}{R_{{\text{EV}}}}&=\left({150 - 108}\right){\text{ million km}}\\&=42{\text{ million km}}\\&=42\times{10^6}{\text{ km}}\\\end{aligned}

The expression for the distance between the Earth from the Jupiter is:

{R_{{\text{EJ}}}} = {R_{{\text{SJ}}}} - {R_{{\text{SE}}}}

Substitute values of {R_{{\text{SJ}}}} and {R_{{\text{SE}}}}.

\begin{aligned}{R_{{\text{EJ}}}}&=({778 - 150})\\&=628\text{ million km}\\&=628\times{10^6}{\text{ km}}\\\end{aligned}

The expression for the distance between the Earth from the Saturn is:

{R_{{\text{ESa}}}} = {R_{{\text{SSa}}}} - {R_{{\text{SE}}}}

Substitute {R_{{\text{SSa}}}} and {R_{{\text{SE}}}} in the above equation.

\begin{aligned}{R_{{\text{ESa}}}}&=({1430 - 150}){\text{ million km}}\\&=1280{\text{ million km}}\\&=1280\times {10^6}{\text{ km}}\\\end{aligned}

Substitute {F_1} for F, 42 \times {10^6}{\text{ km}} for R and the values of {M_1}, {M_2}, M_E and G in equation (1).

{F_1} =\dfrac{{( {6.67 \times {{10}^{ - 11}}})( {5.97 \times {{10}^{24}}})( {0.815 \times 5.97 \times {{10}^{24}}})}}{{{{( {42 \times {{10}^6{\,km}}})}^2}}}

\begin{aligned} {F_1}&=\frac{{( {6.67 \times {{10}^{ - 11}}})( {5.97 \times {{10}^{24}}})( {0.815 \times 5.97 \times {{10}^{24}}})}}{{{{( {42 \times {{10}^9}}} )}^2}}}\\{F_1}&= 0.1098 \times {10^{19}}{\text{ N}}\end{aligned}

Substitute {F_2} for F, 628 \times {10^6}{\text{ km}} for R and values of {M_1}, {M_2}, M_E and G in equation (1).

{F_2}=\dfrac{{( {6.67 \times {{10}^{ - 11}}})( {5.97 \times {{10}^{24}}})( {318 \times 5.97 \times {{10}^{24}}})}}{{{{( {628 \times {{10}^6{\,km}}})}^2}}}

\begin{aligned} {F_2}&=\frac{{( {6.67 \times {{10}^{ - 11}}})( {5.97 \times {{10}^{24}}})({318 \times 5.97 \times {{10}^{24}}})}}{{{{( {628 \times {{10}^9}})}^2}}}\\{F_2}&=0.1916 \times {10^{19}}{\text{ N}}\\\end{aligned}

Substitute {F_3} for F, 1280 \times {10^6}{\text{ km}} for R and the values of {M_1}, {M_2}, M_E and G in equation (1).

\begin{aligned} {F_3}&= \frac{{( {6.67 \times {{10}^{ - 11}}})( {5.97 \times {{10}^{24}}})( {95.1 \times 5.97 \times {{10}^{24}}})}}{{{{( {1280 \times {{10}^9{\,m}}} )}^2}}}\\ {F_3}&= 0.1379 \times {10^{18}}{\text{ N}}\end{aligned}

The force acting on the left side is taken negative and force acting on the left side is taken positive as shown in the redrawn figure.

The expression net force acting on the Earth is:

\fbox{\begin\\F = - {F_1} + {F_2} + {F_3}\end{minispace}}

Here, F is the net Gravitational force acting on the Earth.

Substitute the values in the above equation.

\begin{aligned} F&=-0.1098 \times {10^{19}}+0.1916 \times {10^{19}}+0.1379 \times {10^{18}}\\&= 9.559 \times {10^{17}}{\text{ N}} \\ \end{aligned}

Therefore, the net Gravitational force acting on the Earth \fbox{\begin\\9.559 \times {10^{17}}{\text{ N}}\end{minispace}}.

Learn more:

1. Motion of ball under gravity brainly.com/question/10934170

2. The motion of a body under friction brainly.com/question/7031524

3. Net force on a body brainly.com/question/4033012

Answer Details:

Grade: College

Subject: Physics

Chapter: Gravitation

Keywords:

Every few hundred years, planets, line up, same side, Sun, the Venus, Earth, Jupiter and Saturn, masses, MV=0.815ME, MJ=318 ME and MSat=95.1 ME, mean distance, four planets, 108, 150, 778, and 1430 million km, 9.559x 10^17 N.

You might be interested in
During fusion, atoms are divided.<br> a. True<br> b. False
maksim [4K]
Sorry for answering late! The definition of Fusion is <span>the process or result of joining two or more things together to form a single entity. So that means its False :) </span>
8 0
3 years ago
Read 2 more answers
A 5.0-kg box rests on a horizontal surface. The coefficient of kinetic friction between the box and surface is ????K=0.50. A hor
blagie [28]

Answer:

a)W= 1 J

b)W= 1 J

c)W= 0 J

Explanation:

Given that

m = 5 kg

Coefficient of kinetic friction,K=0.5

d= 10 cm

We know that if velocity is constant it means that the acceleration of the system is zero.Or we can say that all forces are balance in the system.

We know that work is the dot product of force and displacement

W= F.d

The friction force on the box

Fr= K m g

Fr= 0.5 x 5 x 10 = 25 N                      ( take g =10 m/s²)

Fr=25 N

a)

Acceleration a= 0

So horizontal force F = Fr

W = Fr.d

W=10 x 0.1 J

W= 1 J

b)

The work done by friction force

W= 1 J

c)

The net force on the system is zero because acceleration is zero.

F= 0

So

W= 0 J

3 0
3 years ago
Which idea did Ptolemy’s model use to explain why the planets appeared to move backward as they moved in their orbits?
Gnoma [55]

Answer:

The planets spun in epicycles.

Explanation:

4 0
2 years ago
Given f(x)=-2x+7, which of the following is the value of x when f(x)=13?
timama [110]

Answer:

-19 is the answer because put the value of x=13 then make equation

7 0
2 years ago
An object of mass m is attached to the end of a spring and set into oscillation. the period of the oscillation is measured and r
nataly862011 [7]
The answer i think is 1
4 0
3 years ago
Other questions:
  • _____cells do not contain a nucleus
    6·1 answer
  • Both gamma rays and x-rays are used to see inside the body. Which one is used to make images of bones?
    14·2 answers
  • The data table shows some data related to the Sun and the planets in our solar system.
    7·2 answers
  • The graph below shows the velocity of a car over time.
    7·2 answers
  • If a Ball Falls from a girls hand, How does its speed change?
    6·2 answers
  • when an object falls to the ground, only the object moves down but the earth's motion is not noticeable​.why?
    9·1 answer
  • Current can be made to flow in a stationary conductor by ............................
    14·1 answer
  • Describe how a radiation is similar to b- radiation​
    5·1 answer
  • What is the name of the following atoms?
    7·2 answers
  • PLEASE HELP ASAP WILL GIVE BRAINLIEST ​
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!