In gravitational assistance, does the mass matter?

In summary, the mass of the spacecraft does not affect the speed it gains from gravitational assistance from the Sun, as the acceleration is determined by the mass of the Sun and the distance between the Sun and the spacecraft. However, if the spacecraft is significantly more massive than the Sun, its trajectory may be affected.
  • #1
Rodrigo Olivera
29
3
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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  • #2
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?
 
  • #3
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.
 
  • #4
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 .
 
  • #5
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?
 
  • #6
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?
 
  • #7
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.
 
  • #8
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...
 
  • #9
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.
 

1. How does the mass of an object affect gravitational assistance?

The mass of an object plays a crucial role in gravitational assistance. The more massive an object is, the stronger its gravitational pull will be on other objects. This means that a more massive object can provide a greater amount of assistance to another object in terms of altering its trajectory.

2. Is the mass of the object being assisted important in gravitational assistance?

Yes, the mass of the object being assisted is also important in gravitational assistance. This is because the amount of assistance provided by the assisting object is dependent on the mass of the object being assisted. A larger object will experience a greater change in trajectory due to the gravitational pull of the assisting object.

3. Can any object provide gravitational assistance?

Yes, any object with mass can provide some level of gravitational assistance to other objects. However, the amount of assistance provided will vary depending on the mass of the object and its distance from the object being assisted.

4. Does the distance between the assisting object and the object being assisted matter?

Yes, the distance between the two objects does matter in gravitational assistance. The closer the two objects are, the stronger the gravitational pull will be and the greater the change in trajectory experienced by the object being assisted. As the distance increases, the gravitational force decreases and the assistance provided decreases as well.

5. Can multiple objects provide gravitational assistance at the same time?

Yes, it is possible for multiple objects to provide gravitational assistance at the same time. In fact, this is often utilized in space missions to take advantage of the gravitational pull of multiple planets or other celestial bodies in order to alter the trajectory of a spacecraft.

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