MadSci Network: Astronomy Query:

Re: If the sun has enough gravity to orbit comets, then why not the voyager?

Date: Tue Sep 22 10:45:57 1998
Posted By: Everett Rubel, Degree in Physics
Area of science: Astronomy
ID: 904247518.As
Message:
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Dear Tyler,

Thanks for the question.  The answer to it has to do with something called
escape velocity.

In many science fiction movies the characters are often concerned with
escape velocity.  It is treated like a lower limit, and if you cannot reach
it, then your space craft gets pulled into the star, blackhole, or planet
that you are trying to escape.

In real life escape velocity is not some absolute limit that must be
reached in order to avoid a space catastrophe.  It is just the speed a
spacecraft needs so that it can escape an object's gravity by coasting.
One example of a situation like escape velocity is bicycling over a small
hill.  If you want to be able to coast over the hill, you need to have a
certain minimum speed at the bottom of the hill.  This speed is like escape
velocity.  If you don't have enough speed then you stop part way up the
hill and then start to roll backwards, unless you do some work and start
pedaling.

When you talk about escape velocity, you need to make clear what it is that
you are trying to escape.  Also, you have to know how far away you are from
the object.  Rockets launched from Earth's surface  have to reach a speed
of about 11 kilometers a second to be able to coast out into the rest of
the Solar System.  If the rocket starts out near the Moon, then it only
needs about 1.5 kilometers a second of velocity to overcome the pull of the
Earth's gravity.   The force of gravity from an object becomes less the
farther you are from the object, so it becomes easier to escape the
object's gravity.  Escape velocity decreases the farther you are away from
the object.

In the case of the Voyagers and comets, the object that is the main source
of gravitational force is the Sun, as you have pointed out.   Voyager 1 is
currently about 10,600,000,000 kilometers from the Sun, and moving at a
speed of 17.3 kilometers a second away from the Sun.   The escape velocity
of the Sun at that distance is only about 5 kilometers a second, so Voyager
1's speed is well over escape velocity, and it will continue to coast away
from the Sun forever, or until it collides with some other star, planet, or
gas or dust cloud.    At the distance that Voyager 1 is from the Sun, there
are no comets ( that I know of) that even come close to its speed.

Closer in to the Sun the escape velocities are higher.  At Jupiter the
Sun's escape velocity is about 16 kilometers a second.  At Earth, solar
escape velocity is about 43 kilometers a second.  At Mercury, the closest
planet to the Sun, solar escape velocity is about 67 kilometers a second.

Comets spend a lot of time far away from the Sun, moving fairly slowly.  As
comets fall in toward the Sun, the pull of the Sun's gravity increases the
speeds of the comets.  An important fact to keep in mind is that the extra
speed the Sun gives the comets can never be greater than the escape
velocity of the Sun.  So if a comet falls in as far as the orbit of
Mercury, then its speed might be 65 kilometers a second, close to but not
greater than the solar escape velocity at that distance from the Sun.   So
even though the comet's speed is much greater than the speed of Voyager 1,
it does not have escape velocity, because it is closer in toward the Sun.
Near the Sun, where the comets are moving the fastest, is also where the
escape velocity is the greatest.

The planets can make the situation more complicated with comets.   A planet
like Jupiter can greatly affect the motion of a comet, and can even give
the comet an extra boost so that its speed exceeds solar escape velocity.
So sometimes comets do escape the Solar System, just like Voyager 1 is
doing.  In fact this is the method that Voyager 1 used to reach solar
escape velocity.   I think this is called a "sling shot maneuver".

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