Earths gravity

Hi Guys,

I'm trying to gain a basic (and I say basic because I'm not much of a math buff) understanding of what kind of force it takes to launch a rocket \ satellite into space.

From my basic reading - "space" is classified as 100km above earths surface.

What I'm trying to figure out is at what point an object accelerating away from earth stops feeling the effects of earth gravity.

Thanks
Warrick

Related Astronomy and Astrophysics News on Phys.org
Janus
Staff Emeritus
Gold Member
It never stops feeling the effects of Earth's gravity. When you launch an satellite in to orbit you are basically giving it enough speed so that it "falls around the Earth" . The force of gravity at a low orbit height is almost the same as that on the surface. The satelite is traveling so fast (7.9 km per sec), that the Earth's surface curves away just as fast as its path is curved by gravity. It essentially falls towards the earth but keeps missing.

To get an object clear away from the Earth you have to get it moving so fast that, the strength of Earth's gravity falls off faster than it can slow the object. As the object gets further from The Earth the pull of its gravity gets weaker, if the object is moving fast enough, and increases its distance from the Earth fast enough, this gravity can never remove it last bit of speed and it keeps going forever. This speed is called the escape velocity, and from Earth is is about 11 km/ sec.

Thanks Janus,

It looks like the highest satellites that we put into orbit are GPS satellites and fall somewhere between 6,000 - 12,000km above the earth surface. At what distance does gravity become so week that the it stops falling around the Earth?

One would assume that once a rocket gets to this distance that it's fuel consumption become a lot more efficient because it no longer need to battle against earths gravity and have close to no resistance.

I'm sure that other bodies in the sky effect the rocket, but assuming that earth was the only thing out there, would the rocket ever get to a point where it's not effected by earths gravity at all, spurt on last blast of fuel and travel forever into the darkness?

Thanks
Warrick

Thanks Janus,

It looks like the highest satellites that we put into orbit are GPS satellites and fall somewhere between 6,000 - 12,000km above the earth surface. At what distance does gravity become so week that the it stops falling around the Earth?

One would assume that once a rocket gets to this distance that it's fuel consumption become a lot more efficient because it no longer need to battle against earths gravity and have close to no resistance.

I'm sure that other bodies in the sky effect the rocket, but assuming that earth was the only thing out there, would the rocket ever get to a point where it's not effected by earths gravity at all, spurt on last blast of fuel and travel forever into the darkness?

Thanks
Warrick
Communications satellites orbit at 22,300 miles. The moon is a satellite, and orbits at an average of 238,000 miles. A satellite can orbit the until until if falls under the stronger gravitational influence of another body, the Sun for example.

There are a couple of our space probes, at least, that are leaving the Solar System, having enough escape velocity to overcome the combined gravity of the Sun, planets, and other objects that make up the Solar System. So, they have the potential to "travel forever into the darkness," or at least for a long long time.

Good point, I hadn't thought of the moon as a satellite. Much of this came about due to an argument a friend and I were having about getting to Mars. Thought was that it's not that much harder to send something to Mars than it is to send something to the moon.

My view was that once you've got something out in space, it was just as much work to go to Mars as it is to go to the moon. I'm sure I'm way off, but I'd love to know if this is true or not.

HallsofIvy
Homework Helper
Good point, I hadn't thought of the moon as a satellite. Much of this came about due to an argument a friend and I were having about getting to Mars. Thought was that it's not that much harder to send something to Mars than it is to send something to the moon.

My view was that once you've got something out in space, it was just as much work to go to Mars as it is to go to the moon. I'm sure I'm way off, but I'd love to know if this is true or not.
That's largely true but- It is harder to make a soft landing on mars than on the moon because of mars' greater mass, if you are sending people you are going to have to keep them alive for a much longer period, and it will be far harder getting back from mars than from the moon.

cjl
That's largely true but- It is harder to make a soft landing on mars than on the moon because of mars' greater mass, if you are sending people you are going to have to keep them alive for a much longer period, and it will be far harder getting back from mars than from the moon.
Actually, I would think it would be far easier to make a soft landing on mars than the moon. After all, parachutes are quite a bit lighter and less complicated than rockets. That doesn't get rid of the timescale and return issues.

Actually, I would think it would be far easier to make a soft landing on mars than the moon. After all, parachutes are quite a bit lighter and less complicated than rockets. That doesn't get rid of the timescale and return issues.
The atmosphere of Mars is significantly thinner than the Earth's. Comparatively, the atmosphere of Mars (a mere .13 PSI) is less than 1% that of Earth's (14.7 PSI), so parachutes would have to be significantly increased in order to slow a good sized mass from re-entry velocities. This makes a “parachute-only re-entry” a somewhat impractical resolution, as significantly larger parachutes add to the mass of the spacecraft, as well as the greater space required aboard the spacecraft for storage until deployment.

More than likely, a "parachute assist" to a rocket re-entry system would be required.

http://en.wikipedia.org/wiki/Atmosphere_of_Mars

cjl
Yes, but you can still get down to a few hundred meters per second fairly easily, without an excessively large parachute. That's a lot better than the several kilometers per second that you would arrive at the moon with.

Also why should it be harder to get the probe back from mars? Is it because of the greater gravity?

russ_watters
Mentor
It isn't harder to get a probe back from Mars than to send it there. But if you want to get it back, it is even harder to get it there than if you don't want it back.

DaveC426913
Gold Member
Also why should it be harder to get the probe back from mars? Is it because of the greater gravity?
Here's some arbitrary numbers:

Lets say a one-way trip to Mars is a one year voyage.
You have a payload of 20 tons (made of equal parts crew, equipment, food and water).
And let's say the trip requires 80 tons of fuel (4:1 ratio).

OK, how about if we want a return trip?
The trip takes 2 years, so your payload (food, water) increases. So now you payload is 30 tons.

But here's the tricky bit: The trip home needs 80 tons of fuel. That fuel had to be carried to Mars as payload.

Our payload for a return trip to Mars has jumped from 20 tons to (30+80=)110 tons. The amount of fuel for the trip out (at the same 4:1 ratio) is now 440 tons.

Result:
A one-way trip to Mars masses 100 tons.
A return trip to Mars masses 550 tons.

Pengwuino
Gold Member
It looks like the highest satellites that we put into orbit are GPS satellites and fall somewhere between 6,000 - 12,000km above the earth surface. At what distance does gravity become so week that the it stops falling around the Earth?

One would assume that once a rocket gets to this distance that it's fuel consumption become a lot more efficient because it no longer need to battle against earths gravity and have close to no resistance.
It doesn't become that weak. In actuality, you could put a satellite in orbit 30 feet off the surface if you want to. The reason satellites are where they are are various reasons. Some are in particular altitudes because they're synchronized to rotate with the earth (that is, they too have a 24 hour orbital period). I believe communications satellites are typically in geosynchronous orbit. The thing is, once you get into orbit, the only thing that makes a satellite consume fuel (besides course corrections) is the atmosphere slowing it down. You put a satellite into a high enough orbit so that the atmosphere has as low a density as possible that it doesn't create drag on the satellite. At the same time, you want a lower orbit because it takes more energy to put an object in orbit the higher up you want to go. Then of course you add in other factors that are more dependent on what the purpose of the satellite is.

The fact of the matter is even at 6-12k km above the earth's surface, the gravity is still there albeit a fraction of what it is at the earth's surface. A satellite will always be falling towards the earth but since it is in orbit and simultaneously trying to fly away, its "escaping as quickly as its falling" and maintains a stable orbit.

It never stops feeling the effects of Earth's gravity. When you launch an satellite in to orbit you are basically giving it enough speed so that it "falls around the Earth" . The force of gravity at a low orbit height is almost the same as that on the surface. The satelite is traveling so fast (7.9 km per sec), that the Earth's surface curves away just as fast as its path is curved by gravity. It essentially falls towards the earth but keeps missing.

To get an object clear away from the Earth you have to get it moving so fast that, the strength of Earth's gravity falls off faster than it can slow the object. As the object gets further from The Earth the pull of its gravity gets weaker, if the object is moving fast enough, and increases its distance from the Earth fast enough, this gravity can never remove it last bit of speed and it keeps going forever. This speed is called the escape velocity, and from Earth is is about 11 km/ sec.
Thanks janus most informative!

its all about energy and potential.....if enough energy is imparted to a rocket to cross the barrier of earths potential then it escapes its initial bounds....but earths potential extends till infinity.
So we can never fully escape the earths gravitation..but at larger distances much less force would be required to counter it pull.

its all about energy and potential.....if enough energy is imparted to a rocket to cross the barrier of earths potential then it escapes its initial bounds....but earths potential extends till infinity.
So we can never fully escape the earths gravitation..but at larger distances much less force would be required to counter it pull.
Aka

$$F = \frac{G m_1 m_2}{R^2}$$

The larger your radius, the smaller your value of F (mass * gravity of earth). If the universe was just Earth and your rocket, even if you went to distances of hundreds of megaparsecs you'd feel the Earth's gravitation pull. Although I suppose at those distances it would really be more of a tickle :P.

...This speed is called the escape velocity, and from Earth is is about 11 km/ sec.

assuming that an object is launched with only momentum as its pushing (or pulling) force. the space shuttle does not travel that fast-it merely has to have excess thrust in order to overcome gravity, no?

D H
Staff Emeritus
It isn't harder to get a probe back from Mars than to send it there. But if you want to get it back, it is even harder to get it there than if you don't want it back.
It is a whole lot harder to get a probe back from Mars than it is to send it there. Getting to Mars is comparatively easy; it takes less fuel to get something to the surface of Mars (and leave it behind) than it does to get something to the surface of the Moon (and leave it behind). Mars has an atmosphere. There are lots of tricks and techniques that use Mars atmosphere to slow a vehicle down. Aerocapture, aerobraking, parachutes / parasails, balloons, ... all take advantage of Mar's atmosphere to slow a vehicle down with little expenditure of fuel. None of these is available for a lunar landing.

Getting back from Mars is a different story. The outgoing vehicle has to carry the fuel needed for the return mission as dead weight, and this in turn drastically increases the fuel costs for the outgoing flight. The rocket equation is brutal. The landing vehicle has to carry the fuel needed to lift the vehicle back into Mars orbit as dead weight, and this drastically increases the structural and aerodynamic requirements for the landing vehicle. Finally, the return vehicle is coming back to Earth at hyperbolic speeds. This is another very tough problem.

Finally, the return vehicle is coming back to Earth at hyperbolic speeds. This is another very tough problem.

what do you mean by hyperbolic speeds?

D H
Staff Emeritus