In deep space, a small rock orbits an asteroid. The circular, orbit radius (between their center of masses) is 1037 m and the velocity of the rock is 8.02 m/s. Find the mass (kg) of the asteroid. G=6.67x10^-11 m^3/kgs^2.
I got 1.0x10^15 but that is incorrect.
To find the mass of the asteroid, we can use the formula for the centripetal force:
F = (m * v^2) / r
Where:
- F is the centripetal force acting on the rock
- m is the mass of the asteroid
- v is the velocity of the rock
- r is the radius of the circular orbit
The centripetal force is provided by the force of gravity between the rock and the asteroid. So, we can also use the formula for gravitational force:
F = (G * m * M) / r^2
Where:
- G is the gravitational constant (6.67 x 10^-11 m^3/kg/s^2)
- m is the mass of the rock
- M is the mass of the asteroid
- r is the distance between their centers of masses
Since both formulas describe the same force, we can equate them:
(G * m * M) / r^2 = (m * v^2) / r
We can rearrange this equation to solve for the mass of the asteroid (M):
M = (v^2 * r) / (G)
Now we can substitute the known values into the equation to find the mass of the asteroid:
M = (8.02^2 * 1037) / (6.67 x 10^-11)
M = 678059.715 / (6.67 x 10^-11)
M = 1.017542 x 10^16 kg
So the mass of the asteroid is approximately 1.017542 x 10^16 kg.