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# Need the equation for escape velocity de-acceleration

2 replies to this topic

### #1 nickcodybarrett

nickcodybarrett

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Posted 06 December 2018 - 07:03 PM

When traveling outwards to our solar system going above solar escape velocity, what's the rate of de-acceleration? Obviously the sun's gravity is going to slow you down no matter what speed you're going. But how do I calculate that?

Thanks,

Nick

### #2 Brett Waller

Brett Waller

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Posted 06 December 2018 - 08:02 PM

Nick,

I am going to assume you want the simple deceleration at a given radial distance from the Sun, and not the time rate of change of acceleration. I am also going to assume you are not asking for the objects velocity at effectively infinite distance from the Sun. If my assumptions are wrong, please clarify what it is you are seeking.

For an object moving radially away from the Sun, the force of gravitation, F,  at any point would be:

F = (GMm)/r^2

where:

G = Gravitational constant

M = Mass of Sun

m = mass of your object

r = distance from Sun

Since F = ma, simple substitution gives:

ma = (GMm)/r^2 and dividing both sides by m gives the acceleration at that point, thus:

a = (GM)/r^2

Since this is directed opposite to the path of you object, it would normally be expressed as a negative value, which is the deceleration of the object at that distance from the Sun.  I hope this is the value you are seeking.

Brett

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### #3 nickcodybarrett

nickcodybarrett

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Posted 06 December 2018 - 10:44 PM

Thank you it's exactly what I'm looking for!

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