How Many Rockets Would We Need To Launch Into Space To Feel Lighter On Earth?

How many rockets and space equipment would we need to send up before making a change in the earth’s gravity?
Orbits of current Earth-orbiting geophysics satellites. In magenta: TIM (Thermosphere, Ionosphere, Mesosphere) observations; in yellow: solar observations and imagery; in cyan: Geospace and magnetosphere; in violet: Heliospheric observations. At geostationary orbit, GOES and SDO keep watch on the Sun. Image credit: NASA/Goddard Space Flight Center Scientific Visualization Studio

Orbits of current Earth-orbiting geophysics satellites. In magenta: TIM (Thermosphere, Ionosphere, Mesosphere) observations; in yellow: solar observations and imagery; in cyan: Geospace and magnetosphere; in violet: Heliospheric observations. At geostationary orbit, GOES and SDO keep watch on the Sun. Image credit: NASA/Goddard Space Flight Center Scientific Visualization Studio

Originally posed at Forbes!

A lot. The strength of Earth’s gravity is controlled by two fundamental properties of our planet; the distance from the very core of the earth to the surface, and how much mass is held within that space. If our planet were the same size, but made out of packing peanuts instead of rock, the force of gravity at the surface would be much less than it currently is. Similarly, if we took the same amount of material – the same mass – but changed how densely packed it is, you could reduce the pull of gravity on the surface. However, neither of these things is easily changed. The Earth is Earth-sized because it’s mostly made of molten rock and metal, with a bit of liquid water and solid rock on the surface. Molten rock and metal are both pretty hard to compress beyond a certain density, and difficult to fluff up to make it more styrofoam-like (unless you fill it with pockets of gas).

The equation to figure out the strength of gravity on the Earth is pretty simple: g = GM/r^2. M is the mass of the planet, r is the distance from the center to the surface, and G is the gravitational constant, which is a constant feature of our Universe. It’s also a very small number, so it winds up canceling out the very large numbers the Earth is going to dump into this equation. Once we plug in the radius of the Earth and the mass of the earth, we find that gravity on the surface of the Earth is pulling you towards the ground at 9.81 m/s every second.

If we wanted to change the force of gravity, we’d have to reduce this number, which means either increasing the size of the planet (basically impossible), or removing some of its mass (more possible). We have our method of mass removal given in the question, so we’re going to build rocket ships, load them up with stuff, and launch them out into space. How much stuff would we need to remove before the Earth’s gravity changes? Technically, everything we send up removes some mass from the Earth, but it’s such a minuscule fraction of the Earth’s mass that we will never notice the difference. So how much material would we have to send up before we’d notice the difference?

Let’s try and change gravity by ten percent.

This means everyone will feel 10% lighter on the surface, and with the same amount of force, you’d be able to jump higher, and falling would hurt less.

This means we need to reduce the Earth’s gravitational pull from 9.81 meters per second per second to 8.83. If we’re not expanding the distance to the Earth’s surface, the only thing left to change is the mass of the earth, so we’ll have to reduce the Earth’s mass by ten percent. Pretty straightforward.

But the Earth is pretty big. 5.972 × 10^24 kg big. This is a number so outrageously huge that it basically doesn’t make sense to write it in kilograms anymore. We typically write it in “Earth masses” instead, but that’s even less useful for getting a sense of scale. In any case, let’s divide this number to find 10% – there’s some useful scale coming ahead. 10% of the Earth is 5.972 × 10^23 big – one less zero, but twenty three zeros is still a pretty big number.

A comparison of the sizes of Earth and Mars. Image credit: NASA

A comparison of the sizes of Earth and Mars. Image credit: NASA

In fact, it is the mass of Mars. Mars is only slightly more massive than this – with a mass of 6.39 × 10^23 kg, it’s just under 11 percent of the mass of the Earth. So in order to change the gravity of the Earth by a noticeable but not incredibly dramatic ten percent, we would have to extract from the surface of the earth, One Whole Mars worth of material. This, as you can probably guess, would be grossly unwise. If we were to peel off the entire crust of the earth, which is some 3-30 miles deep, and throw in the entire mass of all of the oceans for kicks, we’re still only looking at about a half a percent of the earth’s mass, and we’ve made our planet into Lava Planet. (Never mind the mechanics of peeling off the crust of the Earth, which I can only imagine would go spectacularly poorly.) In fact, in order to get our ten percent, we’d have to extract pretty much the entire upper mantle and jet it into space in order to reduce gravity by 10 percent, and our surface relies on that upper mantle for stability. When the mantle moves, our crust moves with it- which is part of the reason we get earthquakes. Removing that structure from underneath us would be a Grade A Bad Plan.

A NASA/university study of data on Earth’s rotation, movements in Earth’s molten core and global surface air temperatures has uncovered interesting correlations. Image credit: NASA/JPL-Université Paris Diderot – Institut de Physique du Globe de Paris

A NASA/university study of data on Earth’s rotation, movements in Earth’s molten core and global surface air temperatures has uncovered interesting correlations. Image credit: NASA/JPL-Université Paris Diderot – Institut de Physique du Globe de Paris

Of course, beyond the matter of extracting a Mars-worth of magma from the innards of the planet, there’s the slight issue of where to put it.  Mars is not exactly our smallest planetary body, so if we reassembled all of our Earth-extractions into a planet again we might run into some minor orbital disturbances, suddenly having a second Mars hanging around. If we don’t leave it as a single object, but leave it scattered in small pieces, then we have created our very own Asteroid belt.  I would recommend putting your asteroid belt very far away from Earth, or holy space junk Batman, we have created a very hazardous near-Earth environment, which already needs some cleaning.

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Could Aliens See Heat-Based Signs Of Life On Earth?

Could alien spacecraft ever detect “life signs” on a planet against a remotely noisy thermal background? If they were looking for intelligent life wouldn’t it always be easier to look for ordinary radio emissions?
Artificial lights strongly overlap with the concentrations of Earth's population, showing the locations of light pollution. Image credit: Data courtesy Marc Imhoff of NASA GSFC and Christopher Elvidge of NOAA NGDC. Image by Craig Mayhew and Robert Simmon, NASA GSFC

Artificial lights strongly overlap with the concentrations of Earth's population, showing the locations of light pollution. Image credit: Data courtesy Marc Imhoff of NASA GSFC and Christopher Elvidge of NOAA NGDC. Image by Craig Mayhew and Robert Simmon, NASA GSFC

Oh, “life signs.” The Star Trek franchise is probably responsible for this phrase: any planet they arrive near, they scan for signs of life. Sometimes, they scan for signs of intelligent life, or even signs of human life (or a specific alien species). Unfortunately, it’s never quite clear what exactly they’re doing, and the Star Trek: The Next Generation: Technical Manual book has a brief paragraph of incredible technobabble to explain it. (I am delighted that this book exists, by the way.)

Remote lifeform analysis. A sophisticated array of charged cluster quark resonance scanners provide detailed biological data across orbital distances. When used in conjunction with optical and chemical analysis sensors, the lifeform analysis software is typically able to extrapolate a bioform’s gross structure and deduce the basic chemical composition.
Star Trek: The Next Generation Technical Manual

“Charged cluster quark resonance scanners” is completely bogus -- unless a "charged cluster quark" is just a fancy word for a "proton" -- so we can get the Star Trek method out of the way pretty swiftly. And while listening for radio transmissions certainly can work (and is indeed the focus of our current searches for life out there), the success rate of that would also depend on how widespread radio transmissions are (are they still using radio, or do they prefer to beam information through fiber optic cables? Are they advanced enough for widespread radio?) and how much time you have to spend listening. Humans only got to using radio broadly around the 1920s, but there were plenty of intelligent, modern humans around before then. The SETI Institute has plenty of time to listen, though – they have a dedicated telescope just set to listen to what’s out there. Of course, they haven't found anything, while the total amount of radio broadcasts (and even the total power of radio broadcasts) have steadily been on the decline. On the other hand, if you already have a galaxy-exploring spacecraft, you can go hunting for life that isn’t necessarily radio-using at the present time.

We won’t be able to detect that there are precisely 3,000 people living in a given small town – what we can see (both with thermal imaging or with other methods) are the marks that life leaves on the surface of its planet. We’re going to have to use humans and the Earth as our prototype here because we don’t have any other examples, but we have certainly left a series of impacts on our planet. We live in cities, which are distinct in that we’ve cut down trees to build them, and we light them up at night. We build roads between cities, and houses to live in, and we have cleared land to farm.

Denver, Colorado, USA, exhibiting the street grid typical of large cities in the southwestern USA. Image Credit: NASA/ISS

Denver, Colorado, USA, exhibiting the street grid typical of large cities in the southwestern USA. Image Credit: NASA/ISS

How much of the human changes to our planet’s surface you’d be able to see from space depends entirely on the resolution you can achieve with your camera – how small of an object can you spot? Resolution for an image only depends on three things: how close are you to the object in question, what wavelength of light are you looking at, and how many wavelengths of that light you can fit across your telescope. For a heat map, we’re looking in the infrared, from at least orbit around the planet – how much can you see in the infrared?

A heat map of our planet in its entirety looks something like the image below:

The Atmospheric Infrared Sounder (AIRS) instrument aboard NASA’s Aqua satellite senses temperature using infrared wavelengths. This image shows temperature of the Earth’s surface or clouds covering it for the month of April 2003. The scale ranges from -81 degrees Celsius (-114° Fahrenheit) in black/blue to 47° C (116° F) in red. The Intertropical Convergence Zone, an equatorial region of persistent thunderstorms and high, cold clouds is depicted in yellow. Higher latitudes are increasingly obscured by clouds, though some features like the Great Lakes are apparent. Northernmost Europe and Eurasia are completely obscured by clouds, while Antarctica stands out cold and clear at the bottom of the image. Image courtesy AIRS Science Team, NASA/JPL

The Atmospheric Infrared Sounder (AIRS) instrument aboard NASA’s Aqua satellite senses temperature using infrared wavelengths. This image shows temperature of the Earth’s surface or clouds covering it for the month of April 2003. The scale ranges from -81 degrees Celsius (-114° Fahrenheit) in black/blue to 47° C (116° F) in red. The Intertropical Convergence Zone, an equatorial region of persistent thunderstorms and high, cold clouds is depicted in yellow. Higher latitudes are increasingly obscured by clouds, though some features like the Great Lakes are apparent. Northernmost Europe and Eurasia are completely obscured by clouds, while Antarctica stands out cold and clear at the bottom of the image. Image courtesy AIRS Science Team, NASA/JPL

We can see that in general, the poles of our planet show up as cold, and the equator regions as much warmer, but at this resolution, you can’t see any real details. Cities don’t show up here, let alone individual humans. This is due to the combination of the wavelength (the infrared is a longer wavelength than optical light, so the resolution drops), the distance the satellite is orbiting the planet (about 440 miles up), and the size of the collecting area of the satellite.

This image shows the approximate temperature of the land surface (how hot the land would be to the touch) on a summer’s day in Baltimore, Maryland. The highest temperatures are yellow, while cool temperatures are deep purple. The image was made from data collected by the Landsat satellite on August 1, 2001. Image credit: NASA, Robert Simmon, caption text Holli Riebeek

This image shows the approximate temperature of the land surface (how hot the land would be to the touch) on a summer’s day in Baltimore, Maryland. The highest temperatures are yellow, while cool temperatures are deep purple. The image was made from data collected by the Landsat satellite on August 1, 2001. Image credit: NASA, Robert Simmon, caption text Holli Riebeek

You can spot cities via heat measurements; if you’re not in the desert, dense cities tend to be warmer than the surrounding areas – part of this is that we’ve cut down all the trees to build the city; another part is that we've paved it with heat-absorbing asphalt. If the city has a lot of trees planted, this city ‘heat island’ is less obvious. The resolution on these images is about 100 feet, which is still well too large to detect individual people. The resolution here is partially because the size of the mirror on this satellite is still only 16 inches across (not very big, in the scheme of things).

If you just want high resolution, your best bet is to bring a really large mirror & camera (increased collecting area = better resolution), or to swap over to the optical, though clouds will become a problem if you do the second one. On Earth our cloud layer is not very thick, not very hot and tends to move over time, so if you wait long enough you should be able to see what’s underneath any given cloud over time, but if you’re observing a planet more Venus-like in its permanent cloud cover, the optical is not going to be your friend.

On Earth, however, it works fine; commercial satellites in orbit around the earth now can image the Earth down to a resolution of about a foot. (Or at least that’s as good as various militaries will allow them to disclose; super high resolution imagery of the Earth’s surface is also used for military reconnaissance.) With optical high resolution data, you can look for geometric patterns. Perfect circles, squares, rectangles, or triangles are unlikely to happen naturally, so if you spot widespread rectangles on the surface of the Earth, that usually means you’ve found a well-planned city or a farm, either of which indicates some kind of intelligence at work.

This image from Sentinel-2A shows how Saudi Arabia’s desert is being used for agriculture. The circles come from a central-pivot irrigation system, where the long water pipe rotates around a well at the centre. Image Credit: Copernicus Sentinel data (2015)/ESA

This image from Sentinel-2A shows how Saudi Arabia’s desert is being used for agriculture. The circles come from a central-pivot irrigation system, where the long water pipe rotates around a well at the centre. Image Credit: Copernicus Sentinel data (2015)/ESA

Of course, the further away from the planet you are, the harder this is to do - it’s not the sort of scanning you can do while cruising the galaxy at high speeds. To map the whole Earth at low resolution (between ~800 foot and ~3200 foot resolution), the MODIS instrument on one of our earth-orbiting satellites, orbiting at ~450 miles above the surface, takes 2 days. So it’s possible to detect signs of life on a planet via heat images if we’re looking for evidence of cities, but not if we’re looking for individuals, and not if you don’t want to spend a few days in orbit around the planet.

This detailed, photo-like view of Earth is based largely on observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA’s Terra satellite. Image credit: NASA

This detailed, photo-like view of Earth is based largely on observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA’s Terra satellite. Image credit: NASA

Still, if you built a very large aperture, wide-angle telescope, and had it orbiting the planet in space, you just might be able to spot people outside. The Enterprise-D from Star Trek: The Next Generation had a main dish that was approximately 500 meters in diameter, which would give it a resolution about 150 times greater than the Hubble Space Telescope. Even in the infrared, we'd be able to detect individual human beings if we gathered that much light - though to tell that anything was moving, you'd have to take a series of images and play spot the difference. (A series of extremely short exposures would also keep all your images from being blurred into unrecognizability, unless you've parked the Enterprise in geostationary orbit.) If you had an inkling of where to point your dish -- and weren't reliant on mapping the entire planet -- the civilization we've dreamt that Earth becomes in the future may yet be able to spot intelligent life walking around.

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