Calculating Speed of Spacecraft in Gravity Field

[ghostbuster25]

This is a revision question for a test I've got. Just want to check my answer.

An asteroid with mass of 1.8*10¹⁵kg and radius of 6.7km attracts a spacecraft that has come into its gravitational influence. What speed will the spcaecraft crash into the surface. intial speed of spacecraft is negilable.

its a multiply choice and i choose it is impossible to calculate without knowing the mass of the spacecraft .

the equation i would have used is -Gm1m2/r

this right? or is there a way of working out the speed without knowing the mass?

thanks

 

[ehild]

its a multiply choice and i choose it is impossible to calculate without knowing the mass of the spacecraft .

the equation i would have used is -Gm1m2/r

this right? or is there a way of working out the speed without knowing the mass?

Yes, it is a way to find the speed without knowing the mass of the spacecraft .

You said you would have used the equation -Gm1m2/r, but its is not an equation without the other side. What is it equal to?

ehild

 

[ghostbuster25]

well i worked out the gravitaional pull of the asteroid by using Gm1/r^2 and found it to be 0.0026757m/s which makes sense as its a small object. But I am not sure where to go from there as i don't know a, the distance the spacecraft is and b, the mass of the spacecraft so can't use the normal a=f/m

 

[Cyosis]

Hint: Energy conservation: E(infinity)=E(distance at which it impacts the asteroid)

 

[ghostbuster25]

lol I am really lost now

 

[Fightfish]

The total energy (gravitational and kinetic) of the system remains conserved throughout the interaction ie. total initial energy = total final energy.
Basically, use the energy approach in tackling this problem.