70

In order to land on the Moon, you must, at some point, be moving towards the Moon (decreasing your distance from it, to be more precise, you may also be moving sideways) and close enough that the Moon's gravity dominates that of the Earth and the Sun. From that point on, your kinetic energy (relative to the Moon's centre of mass) can only increase as you get ...


67

Your orbit is uniquely determined by a current position (three coordinates) and velocity (three more quantities to give magnitude and direction). Going places involves changing your orbit. For instance, from a circular orbit about Earth, enter an elliptical transfer orbit to the moon, then circularize your orbit about the moon. Everything you do in space ...


58

Going directly to the Moon would require a very small launch window. The Earth orbit before enabled a launch window of about 3 to 4 hours, see this question. Abort from an Earth orbit was possible when the second ignition of the third stage of the Saturn V failed using the Service Module engine to initiate a reentry. Time in orbit was used to complete the ...


56

Yes. 1st scenario: A spacecraft orbiting the Sun at Earth distance vs. Pluto distance, shedding its orbital velocity The orbital velocity decreases with distance, according to the following formula, where $r$ is the orbital radius, and $\mu$ is the mass parameter (it's just a shorthand we use) $$v_{circular} = \sqrt{\frac{\mu}{r}}$$ The orbital velocity ...


54

@SteveLinton's answer is right, no matter how gently you try, by the time you get to the surface the Moon's gravity will have accelerated you to something like 2,400 m/s. There are ways to use the gravity of the Earth and Sun to make a tiny reduction in this, but it's a very small effect. The simplest way to argue this is that rocks on the Moon don't ...


53

I want to allow students to tinker around with basic central force motion and see the ways in which conic sections are altered by thrust, etc. Seeing/enacting an example of rendezvous (maybe in a CW frame?) would be neat too. I definitely think Kerbal Space Program is the right answer here. The ways in which it departs from real-world space flight (such as ...


41

There is very little to gain by going straight to the Moon, and as @Uwe has said, it makes the timing of the launch extremely demanding. Let me have my go at explaining why there is very little to gain. The most fuel efficient way for a rocket to get from Earth to the Moon is basically to accelerate as close to the Earth as possible until it is moving at ...


35

First of all, it can require a lot of computer power to compute trajectories if they involve multiple gravitational slinghots to reduce fuel usage. This isn't because computing each segment is hard but because the search space is at least potentially exponential in the number of gravitational slingshots. I am pretty sure that this is what the thing in The ...


34

To answer your title question: By using its engines. However you seems to be quite puzzled by the fact that velocity of an object can decrease and increase over the course of an orbit. If the orbit is perfectly circular, the speed will always remain the same (until thrusters are used). However, as is the case with Chandrayaan-2, most orbits are ...


26

tl;dr: I don't think there is any scenario where you can strike the Moon with low velocity by using a small impulse to leave orbit. You can hit sideways with an orbital velocity of about 1680 m/s, or vertically with escape velocity the square root of 2 larger at 2376 m/s. Let's say I launched something into lunar orbit with minimal of propellant - just ...


24

Personally, I teach orbital mechanics classes to preschoolers, elementary and middle school kids using a makeshift trampoline with stretchable cloth clamped to the rim. Place a heavy weight (e.g. a dumbell) in the middle to simulate a large massive body like the earth or the sun. Use marbles to illustrate a spacecraft or planets. You can easily show the ...


24

To flyby or impact Venus varies from 3.45 to 3.6 km/s from LEO for the optimal time every 19 months. Mars varies from 3.55 to 3.9 km/s for the optimal time every 26 months. So on average, getting to Venus is a little less energy than getting Mars. But not by much. It could even be a tiny bit more in some years. If you also want to get barely into orbit ...


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

How small do you want to get? $F=G{Mm \over r^2}$ applies regardless of size. If you remove enough disturbances from other bodies you can get two neutrons to orbit a common barycenter on gravity alone - or send them against each other on a near-miss trajectory and they'll pass influencing each other gravitationally in essence performing a slingshot against ...


19

This question seems to hinge on a fundamental misunderstanding about space, that is, to be fair, extremely common among the general public. It's the idea that space has no gravity, so things in space are weightless. "But wait!" you say. "I've seen videos of astronauts in space, and they sure seem weightless to me." And you'd be right, they do seem ...


19

Because the lunar landings happened at some latitude, the landing sites were subject to longitudinal drift due to the Moon's rotation around its own axis. Due to the small latitude of the first landing[1], less than 1 degree for Apollo 11, and the short stay on the Moon, The LM lunar landing site did not drift far from the CSM orbital plane. Hence, Apollo ...


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

All that computing power is not dedicated to the Artemis project. As you quote in the body of your question, The new supercomputer will be used by more than 1,500 scientists and engineers from across the country, including on projects like developing a more efficient quadcopter or simulating the inside of our sun. Not all of this computing power is ...


17

Theoretically, you can go anywhere in GEO for an arbitrarily small ∆v - you raise your apogee a little bit, which slows you down, wait until you've phased to your destination latitude, then re-circularize back into GEO. In practice, though, as @uhoh mentions in comments, there are stable longitudes in GEO that require more than an infinitesimal maneuver to ...


16

Gemini 4 was the first unsuccessful try of a rendezvous. They sought at that times it should be possible to rendezvous from a short distance by simply thrusting towards the docking object. They had to learn it the hard way that this strategy works only on very, very short distances and in a short time. The circumference of a low Earth circular orbit with a ...


16

Sunlight pressure. The acceleration is 9.08 μN / m2 (Assuming perfect reflectivity). The size is about 3.66* 12.6 = 46 m2. That gives a thrust of about 414 uN. The mass is about 1300 kg. Thus the acceleration from sunlight max is about 3.2 e-7 m/s2. Of course, there are a lot of assumptions in that, the mass is probably higher, it won't be perfect ...


16

According to Wikipedia, the delta-v requirements to stay at L1 or L2 are about 30-100 m/s per year. That seems quite high, however, more likely is around 5-16 m/s. The sun shield has an area of about 300 m^2. The thrust possible is about 0.00279664 N, assuming purely reflective. Mass of JWST is about 6200 kg. Putting all of that together, the possible ...


16

I think you may have a misunderstanding that isn't addressed by any of the answers so far. It is true that most of a rocket's work in entering orbit is building up enough speed to reach orbital velocity. But you have to build up even more speed to make it to the moon. In fact, while they were on their way to the moon they were still in orbit around the ...


14

The long comment chain below this answer highlights the mis-conception that NASA astronauts as a whole did not understand the orbital mechanics of docking. As this comment points out, the mechanics was well understood at the time, and at least one astronaut had written a thesis on the topic a few years earlier: ... Aldrins thesis about orbital ...


14

The mass of the Voyager is $\approx$ 825 kg. The mass of the Jupiter is $\approx 1.9 \cdot 10^{27}$ kg. According this question, the Voyager accelerated from $\approx 10.2 \frac{km}{s}$ to $\approx 27.8 \frac{km}{s}$ by its Jupiter flyby at 1979.7.29: Thus, the Voyager got $\approx 17.6 \frac{km}{s}$ velocity from the Jupiter by its gravitational slingshot ...


14

The second table here essentially answers your question. Venus transfer from Low Earth Orbit is 3.5 km/s, Mars transfer is 3.6. This will allow you to impact either body (on Venus you will need to make sure your vehicle is tough enough to actually impact, rather than dissolving in the atmosphere, but that's not really the point). In either case, you can ...


13

There are typically five planned trajectory correction maneuvers on the way to Mars, referred to as TCM-1 to TCM-5. (Also there is a slot for an emergency TCM-6 a few hours before entry, but it is not expected to be used.) Also I sometimes refer to launch as TCM-0. That's the really, really big TCM. TCM-0 provides the energy to place the aphelion of the ...


13

The “westward penalty” from Kennedy/Canaveral would be about 800 m/s of delta-v, about 8-9% of the total delta-v requirement to orbit. Most crewed launchers intended for LEO to date have not had that much performance in reserve; a shortfall of only 100 m/s from LEO usually means prompt reentry. Atlas/Mercury and Titan/Gemini could not have managed it. The ...


12

UC Boulder has a project, PhET, that has many free, interactive, in-browser math and science modules. They have one called Gravity and Orbits that's written in HTML5, making it compatible with most modern browsers (including Safari on iPads). If you click the 'For Teachers' drop-down, you'll find it even has quite a few resources for lesson planning with ...


12

Spaceflight Simulator An Android software, but it's possible to run it on a PC as well. It's 2d, so it's much simpler to use than 3d software. There are some premium features ($4 unlocks all of them forever), but the free version is enough to launch missions to all the planets in the inner Solar System, and to put space stations in orbit and dock to them. ...


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