The planet Mars has two moons, Phobos and Delmos. Phobos has a period of \(7\) hours, \(39\) minutes and an orbital radius of km. The mass of mars is:
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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)
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 about the Earth. What are the changes in the kinetic and potential energies respectively to transfer it to a circular orbit of radius (where is the radius of the earth)
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