Question

Mars has approximately half of the earths diameter. When itis closest to the earth it is at about 1/2 A.U. from the earth.Calculate what size it will appear when seen through the same

telescope.

Answer 1

$$\begin{gathered} Wearegiven, \\ \frac{D_{mars}}{D_{earth}}=\frac{1}{2},whereDisthediameter. \\ Weknow, \\ \frac{D_{earth}}{D_{sun}}=\frac{1}{100} \\ \therefore \frac{D_{mars}}{D_{sun}}=\frac{1}{2}\times \frac{1}{100}=\frac{1}{200} \\ At1A.U.sun\text{'}sdiameter={\frac{1}{2}}^o \\ \therefore mar\text{'}sdiameter=\frac{1}{2}\times \frac{1}{200}=\frac{1^o}{400} \\ At\frac{1}{2}A.U.,mar\text{'}sdiameter=\frac{1}{400}\times 2^o=\frac{1^o}{200} \\ withmagnification=100,mar\text{'}sdiameter=\frac{1}{200}\times {100}^o={\frac{1}{2}}^o=30\text{'} \\ Thisislargerthantheresolutionlimitduetoatmosphericfluctuations.Hence,weconcludethatplanetlooksmagnifiedwhenseenthroughtelescope. \end{gathered}$$