# I In gravitational assistance, does the mass matter?

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1. Apr 23, 2017

### Rodrigo Olivera

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?

2. Apr 23, 2017

### PeroK

What do you think? What do you know about the gravity of the Sun?

3. Apr 23, 2017

### Rodrigo Olivera

I honestly don't know, thats 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. Apr 23, 2017

### PeroK

It doesn't. The Sun is many times more massive than the spacecraft.

5. Apr 23, 2017

### sophiecentaur

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. Apr 23, 2017

### Rodrigo Olivera

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. Apr 23, 2017

### PeroK

Yes.

8. Apr 23, 2017

### Staff: Mentor

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. Apr 25, 2017

### automotiveadam7

Changing "the position of the sun notably" would just affect r?

10. Apr 26, 2017

### jbriggs444

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. Apr 26, 2017

### Staff: Mentor

Yes, and that changes the acceleration and therefore the trajectory of the object.

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