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
Marrrta [24]
3 years ago
15

At what distance from Earth does the force of gravity exerted by Earth on the coasting spacecraft cancel the force of gravity ex

erted by the Moon on the spacecraft? Use the Moon's orbit semimajor axis as a distance between planets.
Physics
1 answer:
telo118 [61]3 years ago
4 0

Answer:

346 * 10⁶ m

Explanation:

The force of gravity of the earth that will cancel the the force of gravity exerted by the moon will be equal to each other

Let F_{e} be the force of gravity exerted by the earth

and let F_{m} be the force of gravity exerted by the moon

According to Newton's law of universal gravitation, the force of attraction between two different masses, m₁ and m₂ separated by a distance, d,  is given by:

F = \frac{Gm_{1} m_{2} }{d^{2} }

Mass of the earth, m_{e} = 5.97 * 10^{24} kg

Mass of the moon, m_{m} = 7.348 * 10^{22} kg

Mass of the satellite, m_{s} = ?

F_{e}  = \frac{G*5.97 * 10^{24} M }{d^{2} }...............................(1)

The earth and the moon are separated by a distance, 3.844 * 10⁸ m

F_{m}  = \frac{G*7.348 * 10^{22} M }{(3.844 * 10^{8} - d) ^{2} }............................(2)

Equating equations (1) and (2)

\frac{5.97 * 10^{24} }{d^{2} } = \frac{7.348 * 10^{24} }{(3.844* 10^{8} -d)^{2} }

(5.97 * 10^{24})(14.78 * 10^{16}  -7.688*10^{8}d + d^{2}) = 7.348 * 10^{24} d^{2} \\88.24*10^{40} - 45.9 * 10^{32}d +  5.97 * 10^{24}d^{2} =  7.348 * 10^{24} d^{2}\\ 1.378 * 10^{24}d^{2} + 45.9 * 10^{32}d + 88.24*10^{40} = 0\\

Factorising out 10^{24}

1.378d^{2} + 45.9 * 10^{8}d + 88.24*10^{16} = 0

Solving for d in the quadratic equation  above:

d = 346 * 10⁶ m

You might be interested in
What are possible units for impulse? Check all that apply.
Neporo4naja [7]

Units of impulse: N • s, kg • meters per second

Explanation:

Impulse is defined in two ways:

1)

Impulse is defined as the product between the force exerted in a collision and the duration of the collision:

I=F\Delta t

where

F is the force

\Delta t is the time interval

Since the force is measured in Newtons (N) and the time is measured in seconds (s), the units for the impulse are

[I] = [N][s]

So,

N • s

2)

Impulse is also defined as the change in momentum experienced by an object:

I=\Delta p

where the change in momentum is given by

\Delta p = m\Delta v

where m is the mass and \Delta v is the change in velocity.

The mass is measured in kilograms (kg) while the change in velocity is measured in metres per second (m/s), therefore the units for impulse are

[I]=[kg][m/s]

so,

kg • meters per second

Learn more about impulse:

brainly.com/question/9484203

#LearnwithBrainly

6 0
3 years ago
Read 2 more answers
14.A 90 kg quarterback gets tackled by being hit by a 120 kg lineman backwards
quester [9]

The acceleration of the quarterback and the lineman is 5.55m/s² and 4.16m/s² respectively in the same direction.

As, we know, the 120 Kg lineman is moving with a force of 500N.

His net acceleration will be in the same direction as his motion.

It is already known that, If M is the mass of the body and a is the acceleration of the body, then the force F on the body can be calculated by using the formula,

F = Ma.

The weight of the quarterback is 90 Kg. He is being hit by a force of 500N.

So, the acceleration can be calculated using the formula,

500N = 90kg x a

a = 5.55 m/s².

Now, the weight if the lineman is 120kg, the force applied by him is 500N.

So, from the formula, his acceleration A will be,

500N = 120Kg x A

A = 4.16 m/s².

both of them will have acceleration in the same direction,

To know more about Force, visit,

brainly.com/question/25239010

#SPJ9

8 0
9 months ago
light of a certain frequency has a wavelength of 438 nm in water.What is the wavelength of this light in benzene​
sveticcg [70]

Answer:

388.97 nm

Explanation:

The computation of the wavelength of this light in benzene is shown below:

As we know that

n (water) = 1.333

n (benzene) = 1.501

\lambda (water) \times n(water) = \lambda (benzene) \times n(benzene)

And, the wavelength of water is 438 nm

\lambda (benzene) = \lambda (water) [\frac{n(water)}{n(benzene}]

Now placing these values to the above formula

So,

= 438 \times \frac{1.333}{1.501}

= 388.97 nm

We simply applied the above formula so that we can easily determine the wavelength of this light in benzene​ could come

5 0
3 years ago
How many electrons must be removed from each of two 5.69-kg copper spheres to make the electric force of repulsion between them
CaHeK987 [17]

Answer:

n=3.056*10^{9} Electrons

Explanation:

Please see attached file

7 0
3 years ago
14. The average speed of a car was 60 m/s by the time it reached the finish line. The car moved in a straight line and traveled
Leni [432]
7.5m. Have a good day :)
4 0
2 years ago
Other questions:
  • If Team 4 wants to increase the horizontal distance that the skittles are projected through the air but keep the height as close
    15·1 answer
  • A fox runs for 12 seconds at a speed of 9.65 m/s. How much distance does it cover? Exact answer, do NOT round.
    9·1 answer
  • Find your mass if a scale on earth reads 650 N when you stand on it.
    13·1 answer
  • Determine the nuclear radius (in fm) for each of the following nuclei.
    7·1 answer
  • ________is what causes acceleration. Two forces acting opposite each other.
    13·1 answer
  • ) What is the electric potential due to the nucleus of hydrogen at a distance of 7.50× 10-11 m? Assume the potential is equal to
    13·2 answers
  • A ballistic pendulum is a device used to measure the speed of projectiles. It consists of a block of wood that hangs from a stri
    11·1 answer
  • Which of the following is a result of sea floor spreading?
    11·2 answers
  • A car crashes into a wall with an impulse of 40,000 kg.m/s. The collision took 2 seconds. How much force did the wall exert?
    7·1 answer
  • In a game of pool, the cue ball moves at a speed of 2 m/s toward the eight ball. When the cue ball hits the eight ball, the cue
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!