The planet Mars has two moons, Phobos and Delmos. Phobos has a period of \(7\) hours, \(39\) minutes and an orbital radius of $9.4\times {10}^3$ km. The mass of mars is:
1. $6.48\times {10}^{23} \mathrm{kg}$
2. $6.48\times {10}^{25} \mathrm{kg}$
3. $6.48\times {10}^{20} \mathrm{kg}$
4. $6.48\times {10}^{21} \mathrm{kg}$

You are given the following data: \(g = 9.81~ \text{m/s}^{2}\), \(R_{E}   =   6 . 37 \times 10^{6}~\text m\), the distance to the moon, \(R = 3 . 84 \times 10^{8}~\text m\) and the time period of the moon’s revolution is 27.3 days. Mass of the Earth \(M_{E}\) in two different ways is:

1.   \(5 . 97 \times 10^{24}  ~ \text{kg and }6 . 02 \times 10^{24}   \text{ kg}\)

2.   \(5 . 97 \times 10^{24}  \text{ kg and }  6 . 02 \times 10^{23}  \text{ kg}\)

3.   \(5 . 97 \times 10^{23}  ~ \text{kg and }6 . 02 \times 10^{24}   \text{ kg}\)

4.   \(5 . 97 \times 10^{23}  \text{ kg and }  6 . 02 \times 10^{23}  \text{ kg}\)

Constant \(k   =   10^{- 13} ~ \text s^{2}~ \text m^{- 3}\) in days and kilometres is?

1.   \(10^{- 13} ~ \text d^{2} ~\text{km}^{- 3}\)

2.   \(1 . 33 \times 10^{14}   \text{ dkm}^{- 3}\)

3.   \(10^{- 13} ~ \text d^{2} ~\text {km}\)

4.   \(1 . 33 \times 10^{- 14} \text{  d}^{2} \text{ km}^{- 3}\)

A \(400\) kg satellite is in a circular orbit of radius \(2R_E\) (where \(R_E\) is the radius of the earth) about the Earth. How much energy is required to transfer it to a circular orbit of radius \(4R_E\)\(?\)
(Given \(R_E=6.4\times10^{6}\) m)
${\mathrm{}}_{}$1. \(3.13\times10^{9}\) J
2. \(3.13\times10^{10}\) J
3. \(4.13\times10^{9}\) J
4. \(4.13\times10^{8}\) J

A 400 kg satellite is in a circular orbit of radius $2{\mathrm{R}}_{\mathrm{E}}$ about the Earth. What are the changes in the kinetic and potential energies respectively to transfer it to a circular orbit of radius $4{\mathrm{R}}_{\mathrm{E}}.$ (where ${\mathrm{R}}_{\mathrm{E}}$ is the radius of the earth)

1. $3.13\times {10}^9 \mathrm{J} \mathrm{and} 6.25\times {10}^9 \mathrm{J}$

2. $3.13\times {10}^9 \mathrm{J} \mathrm{and} -6.25\times {10}^9 \mathrm{J}$

3. $-3.13\times {10}^9 \mathrm{J} \mathrm{and} -6.25\times {10}^9 \mathrm{J}$

4. $-3.13\times {10}^8 \mathrm{J} \mathrm{and} -6.25\times {10}^8 \mathrm{J}$