Question

Find the speed needed to escape from the solar system starting from the surface of Earth. Assume there are no other bodies involved and do not account for the fact that Earth is moving in its orbit. [Hint: Equation 13.6 does not apply. Use Equation 13.5 and include the potential energy of both Earth and the Sun.

a) 11.2 km/s
b) 16.7 km/s
c) 42.4 km/s
d) 61.5 km/s

Answer 1

The speed needed to escape the solar system starting from the surface of Earth is approximately 11.2 km/s.

Step-by-step explanation:

To find the speed needed to escape the solar system starting from the surface of Earth, we can use Equation 13.5, which includes the potential energy of both Earth and the Sun.

The escape speed from Earth's surface is given by the equation:

vesc = √(2GME/RE)

Where vesc is the escape speed, G is the universal gravitational constant, ME is the mass of Earth, and RE is the radius of Earth. Plugging in the values, we get:

vesc = √(2 * 6.67 × 10-11 N m2/kg2 * 5.97 × 1024 kg / 6.37 × 106 m)

Calculating this gives us a speed of approximately 11.2 km/s.

Therefore, the correct answer is option a) 11.2 km/s.