<p>I'm thinking, this is the gist of your question</p>

<blockquote>
  <p>Earth feels a zero net force. Will it help earth to fly away?</p>
</blockquote>

<p>First, zero net gravitational force between two large objects is certainly possible, well, not exactly zero, not for more than an instant anyway, but close to zero, absolutely possible, but whether it leads to an object flying away is more complicated.   It depends on the relative motion of the 3 objects.  </p>

<p>The Moon, for example, orbits the Earth, but from the Moon's point of view, the Sun is about 333,000 times more massive than the Earth and about 388 times further away, (on average) when the Moon is between the Earth and the Sun (390 times when the Moon is on the opposite side of the Earth, again on average.  There's some variation in there).   </p>

<p>Because gravitation drops with the square of the distance, 388 times more distant means about 151,000 times less G force at that relative distance, but with 333,000 times more mass, the Moon actually experiences over twice the gravitational tug from the Sun than it gets from the Earth, so, even though, from the Moon's surface, the Earth is much larger than the Sun, the sun's mass is sufficient to exert the greater gravitational pull.</p>

<p>So, if, by some magical power, you were to grab a hold of the Earth and stop it from moving and grab a hold of the Moon and stop it too, then let the Moon go, the Moon would fall more towards the Sun than the Earth cause the gravitational pull in that direction is over twice as much.   (Ask this great magical being not to let go of the Earth, because if he does, the Earth would fall into the Sun too).</p>

<p>That's not quite the same as your scenario but it points out that zero net gravitation doesn't govern where an object ends up.   The Moon orbits both the Earth and the Sun, and it's in a stable orbit around the earth even though it's feeling more gravitation from the Sun.  That's because the Moon is inside the stable part of the Earth's <a href="https://en.wikipedia.org/wiki/Hill_sphere" rel="nofollow noreferrer">Hill Sphere</a>.  </p>

<p>In your scenario, however, a passing object the mass of another star could certainly pull the Earth away from the Sun.   It wouldn't even need to achieve a net zero gravitation to accomplish that, nor would it need to be nearly so massive.  </p>

<p>The picture below covers the Earth orbiting around the Sun.  If you bring the net Gravity to zero, in theory  the "F" in the diagram shrinks to zero and the Earth continues straight in direction V for that time period, increasing it's distance from the Sun.  <a href="http://physics.bu.edu/~duffy/py105/Gravity.html" rel="nofollow noreferrer">Source</a> </p>

<p><a href="https://i.sstatic.net/YklmL.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/YklmL.gif" alt="http://buphy.bu.edu/~duffy/PY105/Earthsun.GIF"></a></p>

<p>The Earth's tangential velocity relative to the sun is 30 km/s and it's escape velocity is just the square root of 2 times that, about 42.5 km/s, so an acceleration of the Earth of 12.5 km/s or moving the Earth to an orbit a bit outside Mars' orbit and keeping the velocity the same would both work (or some combination of the two).</p>

<p>The model is a bit more complicated because a gravitational assist, which would also happen in your scenario and a gravity assist can work both ways, increasing or decreasing the orbital velocity.  It's possible, depending on direction of the pass, that a passing star could push the Earth closer to the Sun, even passing outside, if it slows the earth's velocity by gravity assist.  Drawing it away isn't the only possible outcome.   </p>

<p>More on gravity assists here, <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/doubal.html" rel="nofollow noreferrer">Short</a> and <a href="https://en.wikipedia.org/wiki/Gravity_assist" rel="nofollow noreferrer">Longer</a>.</p>

<p>As James Kilfinger points out, stars passing that close is extremely extremely rare so this kind of thing, for all practical purposes, virtually never happens.   It's much more rare than a dinosaur killing meteor for example.  It's hugely unlikely.</p>

CC BY-SA 3.0
2015-12-11T05:57:53.960Z
Thank you for such an elaborate answer. I would like to ask is it possible to get earth out of the solar system in this condition?
Bandeep Rabha
CC BY-SA 3.0
2015-12-11T07:48:14.810Z
A star of equal mass passing through the solar-system with (at closest pass) equal gravity on the earth as the Sun, yes it's possible it could pull the earth out of the solar-system.   The precise effect depends on a few factors, if the star is moving with the Earth's direction or in the opposite direction and whether it's on the plane or 90 degrees above the plane and how fast it's moving / how quickly it passes through.  Also, how much the inbound object's orbit is curved by the sun and vise-versa, cause they would affect each other.   Many moving parts to this question.
userLTK
CC BY-SA 3.0
2015-12-11T02:17:22.910Z
2015-12-11T02:17:22.910Z
userLTK
<p>There is no need to hypothesise a black hole. A black hole's gravity is indistinguishable from that of a similarly sized star, except in the region closely surrounding the event horizon.</p>

<p>Black holes can't be only 1 solar mass, there is no known mechanism that could cause a single solar mass object to undergo complete collapse. Black holes have at least three times the mass of the sun.</p>

<p>So could a massive star disrupt the orbit of Earth? <strong>Yes it could</strong>. If the star were to pass by the Earth, it could cause a slingshot effect, transferring some of it's momentum to the Earth, which could cause Earth to leave solar orbit.</p>

<p>In the precise situation that you describe, Earth would initially be travelling in a straight line, but then would follow a complex and possibly chaotic path, as the sun and the black hole pass each other. It is quite possible that the Earth could be ejected, or transferred to an orbit of the black hole in that case.</p>

<p>Fortunately the gaps between stars are so vast (and black holes even more widely spaced) that in the nearly 5 billion years of the Earth, not one has come close enough to cause major disruption to Earth (we know because we are still here).</p>

CC BY-SA 3.0
2015-12-11T06:06:53.310Z
Thank you. is it possible to get earth out of the solar system in this condition?
Bandeep Rabha
CC BY-SA 3.0
2015-12-11T17:09:23.357Z
Please note the paragraph: "So could a massive star disrupt the orbit of Earth? **Yes it could**. ... which could cause Earth to leave solar orbit."
James K
CC BY-SA 3.0
2015-12-11T17:47:59.757Z
"5 billion years...we are still here" do we really know where (orbit) this planet was billions years ago?
jean
CC BY-SA 4.0
2022-08-17T22:21:56.670Z
The difference between a star and a black hole is that the star is clearly there, while the BH might be easy to miss (unless you have material spiraling in), which makes for a better story.
Paŭlo Ebermann
CC BY-SA 3.0
2015-12-10T21:59:04.063Z
2015-12-10T21:59:04.063Z
James K
<p>To escape the Sun's gravity, the Earth would need sufficient amount of energy. Let's say a stellar black hole has entered our solar system and at a certain distance from earth, the black hole exerts same and equal gravitational force on the Earth as the sun is exerting. Earth feels a zero net force. Will it help earth to fly away?</p>

<p>Assuming the black hole had an empty stomach before eating our solar system.</p>

CC BY-SA 3.0
2015-12-10T22:03:52.253Z
Related http://astronomy.stackexchange.com/questions/12296/what-will-happen-if-a-black-hole-appears-near-our-solar-system?rq=1
James K
CC BY-SA 3.0
2015-12-11T00:47:29.193Z
I'm curious about your definition of a black hole with an empty stomach (as opposed to a full stomach)?
userLTK
CC BY-SA 3.0
2015-12-11T06:13:54.063Z
in a reply to "What will happen if a black hole appears near our solar system?" you mentioned that a black hole will have orbital debris like oort cloud and Kuiper belt. I defined it as full stomach. I guessed that there maybe a blackhole who doesn't have orbital debris for now. A fresh blackhole, and empty stomach. Sorry for such lame definitions.
Bandeep Rabha
<solar-system><earth><black-hole><escape-velocity>
Can earth escape sun's gravity with the help of a black hole heading towards our solar system?
Bandeep Rabha
# Can earth escape sun's gravity with the help of a black hole heading towards our solar system?

(Asked by: username_0 on 2015-12-10)

To escape the Sun's gravity, the Earth would need sufficient amount of energy. Let's say a stellar black hole has entered our solar system and at a certain distance from earth, the black hole exerts same and equal gravitational force on the Earth as the sun is exerting. Earth feels a zero net force. Will it help earth to fly away?

Assuming the black hole had an empty stomach before eating our solar system.

**Tags:** solar-system, earth, black-hole, escape-velocity

> **Comments:**
> **username_1**: Related http://astronomy.stackexchange.com/questions/12296/what-will-happen-if-a-black-hole-appears-near-our-solar-system?rq=1  
> **username_2**: I'm curious about your definition of a black hole with an empty stomach (as opposed to a full stomach)?  
> **username_0**: in a reply to "What will happen if a black hole appears near our solar system?" you mentioned that a black hole will have orbital debris like oort cloud and Kuiper belt. I defined it as full stomach. I guessed that there maybe a blackhole who doesn't have orbital debris for now. A fresh blackhole, and empty stomach. Sorry for such lame definitions.  

---

## 2 answers

### Answer by username_2 on 2015-12-11. Score: 1

I'm thinking, this is the gist of your question

> Earth feels a zero net force. Will it help earth to fly away?

First, zero net gravitational force between two large objects is certainly possible, well, not exactly zero, not for more than an instant anyway, but close to zero, absolutely possible, but whether it leads to an object flying away is more complicated. It depends on the relative motion of the 3 objects.

The Moon, for example, orbits the Earth, but from the Moon's point of view, the Sun is about 333,000 times more massive than the Earth and about 388 times further away, (on average) when the Moon is between the Earth and the Sun (390 times when the Moon is on the opposite side of the Earth, again on average. There's some variation in there).

Because gravitation drops with the square of the distance, 388 times more distant means about 151,000 times less G force at that relative distance, but with 333,000 times more mass, the Moon actually experiences over twice the gravitational tug from the Sun than it gets from the Earth, so, even though, from the Moon's surface, the Earth is much larger than the Sun, the sun's mass is sufficient to exert the greater gravitational pull.

So, if, by some magical power, you were to grab a hold of the Earth and stop it from moving and grab a hold of the Moon and stop it too, then let the Moon go, the Moon would fall more towards the Sun than the Earth cause the gravitational pull in that direction is over twice as much. (Ask this great magical being not to let go of the Earth, because if he does, the Earth would fall into the Sun too).

That's not quite the same as your scenario but it points out that zero net gravitation doesn't govern where an object ends up. The Moon orbits both the Earth and the Sun, and it's in a stable orbit around the earth even though it's feeling more gravitation from the Sun. That's because the Moon is inside the stable part of the Earth's [Hill Sphere](https://en.wikipedia.org/wiki/Hill_sphere).

In your scenario, however, a passing object the mass of another star could certainly pull the Earth away from the Sun. It wouldn't even need to achieve a net zero gravitation to accomplish that, nor would it need to be nearly so massive.

The picture below covers the Earth orbiting around the Sun. If you bring the net Gravity to zero, in theory the "F" in the diagram shrinks to zero and the Earth continues straight in direction V for that time period, increasing it's distance from the Sun. [Source](http://physics.bu.edu/~duffy/py105/Gravity.html)

[![http://buphy.bu.edu/~duffy/PY105/Earthsun.GIF](https://i.sstatic.net/YklmL.gif)](https://i.sstatic.net/YklmL.gif)

The Earth's tangential velocity relative to the sun is 30 km/s and it's escape velocity is just the square root of 2 times that, about 42.5 km/s, so an acceleration of the Earth of 12.5 km/s or moving the Earth to an orbit a bit outside Mars' orbit and keeping the velocity the same would both work (or some combination of the two).

The model is a bit more complicated because a gravitational assist, which would also happen in your scenario and a gravity assist can work both ways, increasing or decreasing the orbital velocity. It's possible, depending on direction of the pass, that a passing star could push the Earth closer to the Sun, even passing outside, if it slows the earth's velocity by gravity assist. Drawing it away isn't the only possible outcome.

More on gravity assists here, [Short](http://hyperphysics.phy-astr.gsu.edu/hbase/doubal.html) and [Longer](https://en.wikipedia.org/wiki/Gravity_assist).

As username_1ilfinger points out, stars passing that close is extremely extremely rare so this kind of thing, for all practical purposes, virtually never happens. It's much more rare than a dinosaur killing meteor for example. It's hugely unlikely.

> **Comments:**
> **username_0**: Thank you for such an elaborate answer. I would like to ask is it possible to get earth out of the solar system in this condition?  
> **username_2**: A star of equal mass passing through the solar-system with (at closest pass) equal gravity on the earth as the Sun, yes it's possible it could pull the earth out of the solar-system.   The precise effect depends on a few factors, if the star is moving with the Earth's direction or in the opposite direction and whether it's on the plane or 90 degrees above the plane and how fast it's moving / how quickly it passes through.  Also, how much the inbound object's orbit is curved by the sun and vise-versa, cause they would affect each other.   Many moving parts to this question.  

---

### Answer by username_1 on 2015-12-10. Score: 1

There is no need to hypothesise a black hole. A black hole's gravity is indistinguishable from that of a similarly sized star, except in the region closely surrounding the event horizon.

Black holes can't be only 1 solar mass, there is no known mechanism that could cause a single solar mass object to undergo complete collapse. Black holes have at least three times the mass of the sun.

So could a massive star disrupt the orbit of Earth? **Yes it could**. If the star were to pass by the Earth, it could cause a slingshot effect, transferring some of it's momentum to the Earth, which could cause Earth to leave solar orbit.

In the precise situation that you describe, Earth would initially be travelling in a straight line, but then would follow a complex and possibly chaotic path, as the sun and the black hole pass each other. It is quite possible that the Earth could be ejected, or transferred to an orbit of the black hole in that case.

Fortunately the gaps between stars are so vast (and black holes even more widely spaced) that in the nearly 5 billion years of the Earth, not one has come close enough to cause major disruption to Earth (we know because we are still here).

> **Comments:**
> **username_0**: Thank you. is it possible to get earth out of the solar system in this condition?  
> **username_1**: Please note the paragraph: "So could a massive star disrupt the orbit of Earth? **Yes it could**. ... which could cause Earth to leave solar orbit."  
> **username_3**: "5 billion years...we are still here" do we really know where (orbit) this planet was billions years ago?  
> **username_4**: The difference between a star and a black hole is that the star is clearly there, while the BH might be easy to miss (unless you have material spiraling in), which makes for a better story.  

---

