# Tag Info

134

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 "...

119

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 ...

108

Because the earth goes very fast around the sun. If you want to get to the sun, you need to slow down almost completely so that your speed relative to the sun becomes almost zero. If you don't slow down (almost) completely, your probe will miss the sun when you 'drop' it, so it will eventually come back and you'll end up in an elliptical orbit. Kind of like ...

102

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 ...

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 ...

61

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 ...

47

Delta-V to LEO is about 10 km/s. From there to C3 (Earth escape) is another 3.2 km/s. It's just another 30% delta-V. The problem is the Tyranny of the Rocket Equation. More delta-V means more fuel. More fuel means more mass. More mass means more fuel. How much more? Fuel costs scale according to $e^{\frac{\Delta V}{v_e}}$, that is e to the power of the ratio ...

46

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 ...

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

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, ...

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 ...

36

TL;DR: it is inefficient. You should play some Kerbal Space Program and see for yourself the effects of travel in this way. Assuming, of course, you didn't really want to enter the orbit, but wanted to e.g. go to the Moon or deep space probing. Especially in conjunction with Wikipedia's note about not having to attain escape velocity to leave gravity well....

35

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 ...

34

Changing orbits requires delta-v. To reach the Sun, you need to subtract delta-v such that your velocity relative to the Sun is near zero, which allows you to "fall straight down" into the Sun - your required delta-v is nearly equal to your orbital speed. To escape the solar system, you need to add sufficient delta-v in order to reach escape ...

34

It's not hard, it's just expensive. We know exactly how to do it. Compare this to building computer processors with 1nm transistors, or making reliable self-driving cars. Those are both things that we currently don't know how to do, and we don't even know exactly how to get better at doing them. Even going past low Earth orbit to another planet, like Mars, ...

31

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. ...

31

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 ...

29

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 {... 29 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. 29 The velocity of a rocket can exceed its exhaust velocity. It is possible for the velocity of a rocket to be greater than the exhaust velocity of the gases it ejects. ...The thrust of the rocket does not depend on the relative speeds of the gases and rocket, it simply depends on conservation of momentum. Source https://courses.lumenlearning.com/suny-... 27 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$\Delta v$... 27 An intuitive way to think about it: You have a big rocket, composed of two parts of equal mass: the payload part and the fuel part. You launch the exhaust (fuel) backwards at 1 km/s (for simplicity: all at once so you don't accelerate any of it forward first), and so clearly the payload part is now moving at 1 km/s forward. Open the fairing and reveal the ... 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 ... 23 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},$...

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

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" ...

20

Escaping the solar system requires adding orbital velocity to the spacecraft. Similarly, getting closer in the solar system requires removing orbital velocity. It turns out Earth is more out of the Sun's gravity well than it's in it. In other words, the simple answer is that Mercury is "farther away" in terms of the change of velocity that's ...

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 ...

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