Question 23: Gravitation

Question

A satellite is revolving around the earth in a circular orbit with kinetic energy of $$1.69 	imes 10^{10} \mathrm{~J}$$. The additional kinetic energy required for just escaping into the outer space is

Accepted Answer

To determine the additional kinetic energy required for a satellite to just escape into outer space, we need to understand the relationship between kinetic energy and gravitational potential energy in a circular orbit.
The total energy (E) of a satellite in a stable circular orbit around the Earth is given by:
$$E = \frac{1}{2} mv^2 - \frac{GMm}{r} = -\frac{GMm}{2r}$$
Where:
$$m$$ is the mass of the satellite
$$v$$ is the orbital velocity of the satellite
$$G$$ is the gravitational constant
$$M$$ is the mass of the Earth
$$r$$ is the radius of the orbit of the satellite
The kinetic energy (KE) of the satellite in orbit is:
$$KE = \frac{1}{2} mv^2$$
For a satellite in a stable circular orbit, the kinetic energy is half of the magnitude of the gravitational potential energy, i.e.
$$KE = \frac{GMm}{2r}$$
We know the satellite's kinetic energy is $$1.69 	imes 10^{10} \mathrm{~J}$$.
The total energy (E) will thus be:
$$E = - KE$$
$$E = -1.69 	imes 10^{10} \mathrm{~J}$$
To just escape from Earth's gravity, the total energy should be zero because the satellite would have kinetic energy equal to the gravitational potential energy (but positive because it escapes the gravitational pull). Therefore, the additional kinetic energy required, $$\Delta KE$$, should be equal to the magnitude of the total energy:
$$\Delta KE = 1.69 	imes 10^{10} \mathrm{~J}$$
Thus, the required additional kinetic energy for the satellite to escape into outer space is:
Option B: $$1.69 	imes 10^{10} \mathrm{~J}$$

Answer

$$3.38 	imes 10^{10} \mathrm{~J}$$

Answer

$$1.69 	imes 10^{10} \mathrm{~J}$$

Answer

$$0.89 	imes 10^{10} \mathrm{~J}$$

Answer

$$1.35 	imes 10^{10} \mathrm{~J}$$

Gravitation

A satellite is revolving around the earth in a circular orbit with kinetic energy of $1.69 \times 10^{10} \mathrm{~J}$. The additional kinetic energy required for just escaping into the outer space is

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