124

The force of gravity decreases with distance. It follows an inverse-square relationship... essential to know when you're grinding out the math, but not essential to a conceptual understanding. The fact that gravity decreases with distance means that at some distance, it will be negligible; an object sufficiently distant from Earth may be considered to have "...


95

Escape velocity reduces as you get further away from the Earth. If you proceed upwards at a constant speed of 1 mph (which as noted will require continuous thrust to counteract gravity), you will eventually reach a distance where the escape velocity is equal to 1 mph. Then, you will have reached escape velocity and are no longer gravitationally bound to ...


87

This depends on how much thrust you have available. With enough thrust, you don't need to be in Earth orbit at all: you can launch straight into an escape trajectory. New Horizons did this, more or less: after launch it did about 1/4 orbit before the second stage was ignited again and insertion into its trajectory towards Jupiter began. With very little ...


80

Because linear increases in delta-v require exponential increases in mass, small changes to the assumptions you make about fuel tank structural mass and engine thrust-to-weight ratio start to make very large changes in the final size of the rocket. For example, if you're getting off a 3.6g planet with a 7-stage rocket, the difference between 88% fuel ...


74

Of the 533 humans who have been in orbit, have any of them been sent into space with enough propellant to actually escape Earth's grasp, should they have chosen to use the fuel in that manner? Has any human ever had the choice to never return to Earth? Apart from the Apollo missions, no crewed spacecraft has had anything like enough propellant to leave ...


60

To sum up the answers: the escape velocity is the velocity that, at a given distance, is sufficient to escape the gravitational field so that no additional energy (= acceleration) is needed. That is, if you are 26000 AU from Earth, you don't need any more fuel to counteract Earth's gravity, you just float away. However, when at Earth's surface, you will ...


46

Zero See at: https://en.wikipedia.org/wiki/Escape_velocity for theory. Once you build enough velocity to surpass gravitational attraction, you will leave planetary orbit. A spacecraft simply circling the earth in orbit is not inherently doing anything to contribute to escaping that orbit.


46

why weren't they completely attracted by their gravitational field? How much a trajectory is changed, depends on 3 factors: the mass of the planet, the speed of the spacecraft, the distance between spacecraft and planet Voyager's speed and distance were chosen to make sure Voyager wouldn't enter orbit around the planet. Voyager's speed before approaching ...


43

http://nbviewer.jupyter.org/gist/leftaroundabout/3955d27877e19be39d0f61fdafce069e Barely achieving escape velocity means you take a parabolic orbit. The thing with parabolic orbits is that they actually approach zero speed as you depart to infinite distance from the starting body. That is, zero speed with respect to the starting body's frame of reference, ...


36

The answer to your title question "Why not travel to Mars in 2 months?" has already been answered. Money. Lots and lots of money. We should first note that the answer to a different question: "Why haven't people gone to Mars?" is much the same. Money. However the amount of money to go there in two months is many times greater than the money to go there ...


33

You are confusing velocity and acceleration. If you were to jump standing on the surface of the Earth you might experience 8 m/s which is 17 mph velocity upward, but the acceleration of gravity would act to retard your motion, slowing your velocity down. If you have a high enough velocity, the effect of (de) acceleration can not slow you down ...


30

Soyuz 11 The crew did not return to Earth in their lifetimes. This interpretation is obviously not what you are talking about though. Instead what is of interest is human's remains that do not return to Earth ever. In this case there is also a definitive answer. Clyde Tombaugh Tombaugh died on January 17, 1997, when he was in Las Cruces, New Mexico, at ...


27

Wikipedia gives $0.51 {km \over s}$ or $510 {m \over s}$ escape velocity, so, no, no leaving Ceres by jumping. Following my earlier calculations, an asteroid of the radius of Ceres would have orbital speed at near-surface orbit of about $336 {m\over s}$, which is way beyond jump strength of anyone as well. Gravitational acceleration on the Moon is $1.6249 {...


27

You are correct that Voyager did not change from above escape velocity to below escape velocity shortly after launch. The plot is misleading in that it is just not very accurate right there at 1 AU. The plot lines are kind of thick and a smidge off. Now that I look at it more closely, the escape velocity line in that plot is wrong in other places as well. ...


25

I think if you are powered (rocket/motor ) you can go at any speed and escape the gravity. The escape velocity is only for objects thrown (projected into space), with the initial velocity and they are not powered.


24

First, let us look at the rocket equation: $$\Delta v=\ln \left(\frac{m_0}{m_f}\right)v_e$$ That tells how much a rocket can change its velocity (the $\Delta v$). The requirements for reaching a higher velocity for a minimal orbit would increase on your heavier Earth. (For constant density it is proportional to the radius.) How can we increase the $\Delta ...


24

Think of this as a slightly different question, and the answer becomes more clear. How many times do you have to circle the Sun to leave orbit? The Earth has been orbiting our Sun for about 4.5 Billion years with each year being one orbit. The Earth is expected to stay in orbit around the Sun for the next few billion years. Also consider the moon has ...


22

The most fuel efficient way to leave the solar system at present, is to launch into a trajectory that (like that used for Gallileo) may well involve one or several gravity assists from Earth or Venus, but which eventually gets you to Jupiter. If you can get to Jupiter you can almost certainly do so in such a way as get a slingshot into a solar escape ...


21

tl;dr: No chance, not even close! The escape velocity from the surface of a round (spherically symmetric) body is given by $$v_{esc} = \sqrt{\left(\frac{2 GM}{r_0} \right)}, $$ showing that it is the $\frac{mass}{radius}$ ratio that's key here, not just the surface gravity given by $$a_{g} = -\frac{GM}{r_0^2}. $$ So since $$v_{esc} = \sqrt{a_g r_0}, $...


21

To add to the answers @Hobbes & @Steve Linton posted, the mission designers indeed knew Jupiter's gravity field quite well from the orbits of Jupiter's moons. But before the Voyagers arrived they got additional measurements from the close flybys of two other spacecraft, Pioneers 10 and 11. @Steve Linton correctly describes the effect of the "sideways" ...


19

Why zero excess velocity? Well, with almost zero excess velocity you can stay near Earth, but not too near. For example, the Spitzer space telescope did this to communicate with Earth while avoiding radiant heat from Earth. It's been drifting away, but slowly enough that other factors first reduced its effectiveness.


18

This is actually pretty difficult to do, because it depends on where from due to uneven distribution of matter (local parameters), how far from the galactic center due to radial velocity, the direction in which you want to reach escape velocity (how much of the radial velocity can be used), and that it's hard to estimate mass of the Milky Way (global ...


18

It is absolutely possible, just not advised. New Horizons was launched at Solar System Escape Velocity, meaning it could have visited anywhere beyond Earth without stopping. It did visit Jupiter, however, that was to allow it to leave even faster, the Jupiter stop was purely optional. As for the issue of human capable spacecraft, again, it could be done, if ...


16

The image (original at Wikimedia Commons) is only an approximation, as evidenced by the noticeable change in shape of the solar system escape velocity line at 14AU. The line is only defined with three points, and my guess would be that the creator of the graph tried to shape the curve manually. According to Wikipedia the solar system escape velocity at the ...


15

As @Rikki-Tikki-Tavi points out escape velocity is the velocity you would need at (or near) the surface of Earth to make out out of Earth orbit. Of course, just like anything thrown up into the air, the spacecraft decelerates as it moves away from the Earth. Having escape velocity means that your total energy (relative to the Earth in this case) is greater ...


15

It would be lost in space. If you barely reached the moon escape velocity, it means that your object will reach an orbit somewhat similar to that of the moon. From there, the orbit will be unstable due to earth/moon (and other bodies) interactions. It might take the cargo back earth, back to the moon, or in deep space. Predicting accurately theses orbits ...


15

Let's try and understand how gravity works in space. This is kind of key idea to understanding lots of issues in space travel and astronomy. So imagine a space probe, or rock, which is heading in from deep space, aimed almost, but not quite towards a planet. We can break that motion into two parts -- the part towards the planet and the "sideways" part. The ...


14

Escape velocity is the speed at which you'll leave the Earth and not return if you don't continue to propel your craft. Below that speed, gravity will pull you back down. If you want to keep propelling your rocket vertically at 1 m/s for 100,000 seconds, you'll need an indescribably vast amount of fuel to do so, because you have to maintain sufficient ...


13

What's your engineering budget? This is a hideously impractical undertaking. Most of the mass of an orbital rocket is fuel and the tanks to hold it; even though your payload is tiny, all the rest of that stuff is big. The smaller a rocket is, the harder it is to design it with the high fuel-mass-to-dry-mass ratio that is required to attain high speeds, ...


13

Definitely - it could be ejected. But Earth would only play a minor role. Starman now counts as a Near Earth Object, being any object crossing Earth's orbit. Any such object is occasionally in Earth's vicinity, when they cross our orbit while we are nearby. The orbits of such objects have now been modeled over time periods of millions of years. From ...


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