An asteroid with mass m = 1.85*10^9 kg comes from deep space, effectively from infinity, and falls toward Earth. How much work would have to be done on the asteroid by friction to slow it to 550 m/s by the time it reached a distance of 1.50*10^8 m from Earth?

To calculate the work done by friction on the asteroid, we need to determine the initial energy of the asteroid when it is at infinity and the final energy when it is at a distance of 1.50*10^8 m from Earth. The work done is then the difference between these two energies.

1. Calculate the Initial Energy:
The initial energy of the asteroid when it is at infinity is given by its kinetic energy. Since it is essentially at rest, the initial kinetic energy is 0.

2. Calculate the Final Energy:
The final energy of the asteroid includes both its kinetic energy and gravitational potential energy when it is at a distance of 1.50*10^8 m from Earth.

a. Calculate the final kinetic energy:
The final kinetic energy is given by the formula:
KE = (1/2) * m * v^2
where m is the mass of the asteroid and v is its final velocity.

Plugging in the values:
m = 1.85*10^9 kg
v = 550 m/s

KE = (1/2) * (1.85*10^9 kg) * (550 m/s)^2

b. Calculate the final potential energy:
The final potential energy is given by the formula:
PE = - G * (m * M) / r
where G is the gravitational constant, m is the mass of the asteroid, M is the mass of the Earth, and r is the distance between the asteroid and Earth.

Plugging in the values:
G = 6.67430 × 10^(-11) m^3 kg^(-1) s^(-2)
m = 1.85*10^9 kg
M = 5.972 × 10^24 kg
r = 1.50*10^8 m

PE = - (6.67430 × 10^(-11) m^3 kg^(-1) s^(-2)) * ((1.85*10^9 kg) * (5.972 × 10^24 kg)) / (1.50*10^8 m)

Now, sum up the final kinetic energy and potential energy to get the final energy of the asteroid at a distance of 1.50*10^8 m from Earth.

3. Calculate the Work Done:
The work done by friction is the change in energy of the asteroid. Therefore, the work done is the difference between the final energy and the initial energy.

Work = Final Energy - Initial Energy

Now, substitute the values and calculate the work done by friction.

Please note that this calculation assumes no other external forces are acting on the asteroid, such as air resistance or other gravitational forces.