Question

Read the following paragraphs and write the answers.

Next to the moon, the astronomical object nearest to the earth is Mars. Many nations sent spacecrafts to Mars. Mars mission is difficult and almost half the missions were unsuccessful. However, ISRO’s performance in this mission is remarkable and we all must be proud of it. The spacecraft ‘Mangalyaan’ made by ISRO using minimum expenses was launched in November, 2013 and was placed into orbit around Mars in September, 2014. It obtained very useful information about the surface of Mars and the atmosphere around it.

1. Next to the moon, which is the nearest celestial object to the earth?
2. When did Mangalyaan placed into orbit around Mars by ISRO?
3. What important information did ISRO's Mangalyaan obtain?
4. Explain that critical velocity does not depend on the mass of the satellite.

Answer 1

1. Next to the moon, mars is the nearest celestial object to the earth.
2. Mangalyaan was placed into orbit around Mars by ISRO in September 2014.
3. ISRO’s Mangalyaan obtained very useful information about the surface of Mars and the atmosphere around it.
4. Consider the satellite of mass m revolving at height h around the planet of mass M and radius R with speed v as shown in the figure given above. As the satellite is moving in a circular orbit, a centripetal force acting on it is provided by the gravitational force of the planet,
   i.e., `"mv"^2/"r" = "GMm"/"r"^2`
   But r = R + h
   ∴ `"v"^2 = "GM"/("R + h")`
   ∴ `"v" = sqrt("GM"/"R + h")`
   Hence, critical velocity does not depend on the mass of the satellite.