# physics

posted by .

i posted this earlier but am now stuck on getting through the algebra

1. The problem statement, all variables and given/known data

13) (II) At what distance from the Earth will a spacecraft on the way to the Moon experiance zero net force due to these two bodies becasue the Earth and Moon pull with equal and opposite forces?

2. Relevant equations

NET F = ma
G = 6.67 E-11 (Nm^2)/kg^2
Fg = (GmM)/r^2
Mass Moon = 7.35 E 22 kg
Mass Earth = 5.98 E 24 Kg
r Earth to Moon = 384,403,000 m

3. The attempt at a solution

Apply Newton's s second law in the radial direction

NET F = m_craft( a_radial) = Fg moon = Fg Earth = 0
= (G m_craft m_moon)/(384,403,000 m - r)^2 = (G m_craft m_Earth)/r^2

m_craft cancels
G cancels

m_moon/(384,403,000 m - r)^2 = m_Earth/r^2
simplify

m_moon/((384,403,000 m)^2- r^2) = m_Earth/r^2

raise both sides to negative one power

((384,403,000 m)^2- r^2)/m_moon = r^2/m_Earth

multiply both sides by m_Earth

m_Earth( (384,403,000 m)^2 - r^2 )/m_moon = r^2

simplify

( m_Earth(384,403,000 m)^2 - m_Earth(r^2) )/m_moon = r^2

simplify further

(m_Earth * (384,403,000 m)^2)/m_moon - (m_Earth (r^2) )/m_moon = r^2

add (m_Earth (r^2) )/m_moon to both sides

(m_Earth * (384,403,000 m)^2)/m_moon = (m_Earth (r^2) )/m_moon + r^2

I don't know were to go from here...

• physics -

I believed this is correct after noticing my mistake

Ok I'm here what do I do now

0 = (m_M r^2)/m_E + r^2 + 2(3.84403 m)r - (3.84403E9 m)2

• physics -

sorry

0 = (m_M r^2)/m_E + r^2 + 2(3.84403 m)r - (3.84403E9 m)^2

• physics -

sorry again

0 = (m_M r^2)/m_E + r^2 + 2(3.84403 E 8 m)r - (3.84403 E8 m)^2

• See other post -

## Similar Questions

1. ### Physics

I have no idea how to do this problem At what distance from the Earth will a spacecraft on the way to the Moon esperience zero net force due to these two bodies because the EArth and Mon pull with equal and opposite forces?
2. ### physics

can you walk me through this problem At what distance from the Earth will a spacecraft on the way to the Moon esperience zero net force due to these two bodies because the EArth and Mon pull with equal and opposite forces?
3. ### Physics

I'm not sure how to go about solving this problem the algebra gets very messy... At what distance formt he EArth will a spacecraft on the way to the Moon experiance zero net force due to there two bodies because the Earth and Moon …
4. ### Physics

1. The problem statement, all variables and given/known data The asteroid Icarus, though only a few hundred meters across, orbits the Sun like the other planents. Its period is about 410 d. What is its mean distance from the Sun?
5. ### physics

When a spacecraft travels from Earth to the Moon, the gravitational force from Earth initially opposes this journey. Eventually, the spacecraft reaches a point where the Moon's gravitational attraction overcomes the Earth's gravity. …
6. ### Physics

When a spacecraft travels from the Earth to the Moon, both the Earth and the Moon exert a gravitational force on the spacecraft. Eventually, the spacecraft reaches a point where the Moon's gravitational attraction overcomes the Earth's …
7. ### physics

A spacecraft of mass is first brought into an orbit around the earth. The earth (together with the spacecraft) orbits the sun in a near circular orbit with radius ( is the mean distance between the earth and the sun; it is about 150 …
8. ### physics

A Titan IV rocket has put your spacecraft in a circular orbit around Earth at an altitude of 230 km. Calculate the force due to gravitational attraction between the Earth and the spacecraft in N if the mass of the spacecraft is 2300 …
9. ### maths

The Weight of an object varies inversely as the square of its distance from the centre of the earth.the weight of a spacecraft is observed to be only a quater of its weight on earth.How far is the spacecraft from the surface of the …
10. ### Physics

A rocket has put your spacecraft in a circular orbit around Earth at an altitude of 350 km. Calculate the force due to gravitational between the Earth and the spacecraft in N if the mass of the spacecraft is 2450 kg.

More Similar Questions