In gravitational assistance, does the mass matter?

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Discussion Overview

The discussion centers around the influence of spacecraft mass on the speed achieved through gravitational assistance, specifically in the context of the Helios 2 spacecraft's interaction with the Sun. Participants explore theoretical implications and the underlying physics of gravitational forces and acceleration.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants question whether the mass of the spacecraft affects its speed after gravitational assistance, particularly comparing a 100 kg spacecraft to one with a mass of 10,000 tons.
  • One participant asserts that the mass does not matter because the Sun's mass is significantly greater than that of the spacecraft.
  • Another participant raises the gravitational force formula, suggesting that the force depends on the mass of both objects, prompting further inquiry into how this affects acceleration.
  • A participant explains that the acceleration experienced by the spacecraft does not depend on its mass, indicating that all spacecraft would reach the same final speed under the same initial conditions.
  • Concerns are raised about scenarios where a spacecraft's mass could notably affect the Sun's position, which would alter the assumptions used in calculating trajectories.
  • Further clarification is provided that changing the Sun's position would affect the distance to the barycenter of the sun/craft system and thus impact the trajectory and acceleration of the spacecraft.

Areas of Agreement / Disagreement

Participants express differing views on the influence of spacecraft mass on speed after gravitational assistance. While some argue that mass does not matter, others question this assertion and explore the implications of gravitational forces.

Contextual Notes

Participants discuss the gravitational force and acceleration in theoretical terms, with some assumptions about the mass of the Sun and the spacecraft. The discussion includes considerations of how significant mass changes could affect gravitational interactions and trajectory calculations.

Rodrigo Olivera
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The spacecraft "Helios 2" (with 100 kg of mass) used the Sun to get a speed of 250.000 km/h using gravitational assistance, I want to know if the mass of the spacecraft influences the result of the speed. I mean, if the spacecraft mass 10.000 tons, the speed would be less of more?
 
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Rodrigo Olivera said:
The spacecraft "Helios 2" (with 100 kg of mass) used the Sun to get a speed of 250.000 km/h using gravitational assistance, I want to know if the mass of the spacecraft influences the result of the speed. I mean, if the spacecraft mass 10.000 tons, the speed would be less of more?
What do you think? What do you know about the gravity of the Sun?
 
PeroK said:
What do you think? What do you know about the gravity of the Sun?
I honestly don't know, that's why I'm asking. I just want to know if the mass of spacecraft affects the speed of this one after the gravitational assistance.
 
Rodrigo Olivera said:
I honestly don't know, that's why I'm asking. I just want to know if the mass of spacecraft affects the speed of this one after the gravitational assistance.
It doesn't. The Sun is many times more massive than the spacecraft .
 
Rodrigo Olivera said:
I honestly don't know, that's why I'm asking. I just want to know if the mass of spacecraft affects the speed of this one after the gravitational assistance.
What is the formula for working out the Gravitational force on an object, from another Mass? Isn't the force dependent on the mass of both objects? Do a bit of Googling if you don't know the answer to that one.
Edit: and then what acceleration will this force cause to your ship?
 
PeroK said:
It doesn't. The Sun is many times more massive than the spacecraft .
You mean that it doesn't matter if the spacecraft mass is 10.000 tons or 100kg? The sun will give 70km/s of speed to the spacecraft anyway?
 
Rodrigo Olivera said:
You mean that it doesn't matter if the spacecraft mass is 10.000 tons or 100kg? The sun will give 70km/s of speed to the spacecraft anyway?

Yes.
 
The gravitational force on the spacecraft is ##F=\frac{GMm}{r^2}## with the gravitational constant G, the mass of the sun M, the mass of the spacecraft m and the distance r. Newton's second law tell us that ##F=ma##, and plugging that into the first equation we get ##a=\frac{GM}{r^2}##: The acceleration does not depend on the spacecraft mass. At the same initial speed, every spacecraft will reach the same final speed.

This stops working if the spacecraft is so massive that it changes the position of the sun notably, but then it has to be more massive than Jupiter...
 
mfb said:
This stops working if the spacecraft is so massive that it changes the position of the sun notably, but then it has to be more massive than Jupiter...

Changing "the position of the sun notably" would just affect r?
 
  • #10
automotiveadam7 said:
Changing "the position of the sun notably" would just affect r?
Changing the position of the sun (for example) notably would affect the simplifying assumptions on which a trajectory would usually be calculated. Instead of orbiting the Sun under a force that is given by Newton's universal law of gravity based on the mass of the Sun and the distance to its center, the craft would be orbiting the barycenter of the sun/craft system under a force based on the distance to that barycenter and a reduced effective solar mass.
 
  • #11
automotiveadam7 said:
Changing "the position of the sun notably" would just affect r?
Yes, and that changes the acceleration and therefore the trajectory of the object.
 

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