Receiving Helpdesk

what is the relationship between a stars temperature and its brightness

by Heather Krajcik Published 3 years ago Updated 2 years ago

What is the relationship between a star's temperature and its brightness? A star's brightness, or luminosity, depends on the star's surface temperature and size. If two stars have the same surface temperature, the larger star will be more luminous.

" The Luminosity of a star is proportional to its Effective Temperature to the 4th power and its Radius squared." Example 1: Two stars are the same size, (RA=RB), but star A is 2x hotter than star B (TA=2TB): Therefore: Star A is 24 or 16x brighter than Star B.

Full Answer

What determines the brightness of a star?

A star's brightness, or luminosity, depends on the star's surface temperature and size. If two stars have the same surface temperature, the larger star will be more luminous. The Hertzsprung-Russell (H-R) diagram below is a scatter plot that shows the relative temperatures and luminosities of various stars. Click to see full answer.

What is the relationship between temperature and luminosity of stars?

See the sidebar for a formula to that shows how a star's luminosity is related to its size (radius) and its temperature. This is the relationship between luminosity (L), radius (R) and temperature (T): L = (7.125 x 10-7)R2T4 where the units are defined as L - watts, R - meters and T - degrees Kelvin

Why are some stars brighter than others?

When you look at the night sky, you can see that some stars are brighter than others as shown in this image of Orion. Two factors determine the brightness of a star: Advertisement. luminosity - how much energy it puts out in a given time.

What is the relationship between luminosity radius radius and temperature?

This is the relationship between luminosity (L), radius (R) and temperature (T): L = (7.125 x 10-7)R2T4 where the units are defined as L - watts, R - meters and T - degrees Kelvin 1 … 3 4 5 … Cite This!

What is the relationship between a star and its brightness?

The apparent brightness of a star is proportional to 1 divided by its distance squared. That is, if you took a star and moved it twice as far away, it would appear 1/4 as bright; if you moved it four times the distance, it would appear 1/16 as bright.

Does size and temperature of a star affect its brightness?

For two stars of identical size and temperature, the closer one to us will appear brighter. An analogy is a row of street lights, the closer ones appear much brighter than those in the distance.

What is the relationship between temperature and color and brightness?

Brightness clearly increases with temperature and with any incandescent (glowing from heat) object the hotter the object the bluer its light. What makes a star hotter is a more rapid rate of fusion in the core which is driven by higher pressure from higher mass.

What affects the brightness of a star?

The apparent brightness of a star depends on both its luminosity and its distance from Earth. Thus, the determination of apparent brightness and measurement of the distance to a star provide enough information to calculate its luminosity.

What causes the brightness of a star?

A star's brightness also depends on its proximity to us. The more distant an object is, the dimmer it appears. Therefore, if two stars have the same level of brightness, but one is farther away, the closer star will appear brighter than the more distant star - even though they are equally bright!

What is the relationship between temperature color and brightness of most stars as seen in the main sequence stars?

The mass and luminosity of a star also relate to its color. More massive stars are hotter and bluer, while less massive stars are cooler and have a reddish appearance. The sun falls in between the spectrum, given it a more yellowish appearance.

Does color temperature affect brightness?

Generally, the higher the Degrees Kelvin, the whiter the color temperature of the bulb. Although the whiter lights will appear “brighter” than those of a lower Kelvin reading, the amount of lumens on the brightness scale does not change, and true brightness is not affected.

Are hotter stars brighter?

Stars on the Main Sequence that are hotter than the Sun are also larger than the Sun. So hot blue stars are more luminous (and therefore appear higher in this diagram) for two reasons: they are hotter, and hot objects are more luminous than cool objects, but they are also larger.

What determines the brightness of a star?

Two factors determine the brightness of a star: 1 luminosity - how much energy it puts out in a given time 2 distance - how far it is from us

How to measure the brightness of a star?

Astronomers (professional or amateur) can measure a star's brightness (the amount of light it puts out) by using a photometer or charge-coupled device (CCD) on the end of a telescope. If they know the star's brightness and the distance to the star, they can calculate the star's luminosity: [luminosity = brightness x 12.57 x (distance)2].

How does a searchlight determine the brightness of a star?

Two factors determine the brightness of a star: A searchlight puts out more light than a penlight. That is, the searchlight is more luminous. If that searchlight is 5 miles (8 kilometers) away from you, however, it will not be as bright because light intensity decreases with distance squared.

What does a larger star mean?

The larger a star is, the more energy it puts out and the more luminous it is. You can see this on the charcoal grill, too. Three glowing red charcoal briquettes put out more energy than one glowing red charcoal briquette at the same temperature. Likewise, if two stars are the same temperature but different sizes, ...

What happens if two stars are the same temperature but different sizes?

Likewise, if two stars are the same temperature but different sizes, then the large star will be more luminous than the small one. See the sidebar for a formula to that shows how a star's luminosity is related to its size (radius) and its temperature.

What is the name of the star that is brighter than others?

The constellation Orion as seen from the space shuttle Endeavour (STS-54) Photo courtesy NASA. When you look at the night sky, you can see that some stars are brighter than others as shown in this image of Orion. Two factors determine the brightness of a star: Advertisement.

Is a searchlight brighter than a penlight?

That is, the searchlight is more luminous. If that searchlight is 5 miles (8 kilometers) away from you, however, it will not be as bright because light intensity decreases with distance squared. A searchlight 5 miles from you may look as bright as a penlight 6 inches (15 centimeters) away from you.The same is true for stars.

image
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 2 3 4 5 6 7 8 9
8.3.21PHP Version672msRequest Duration2MBMemory UsageGET {post}Route
  • warninglog[17:51:53] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[17:51:53] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[17:51:53] LOG.warning: Callables of the form ["Swift_SmtpTransport", "Swift_Transport_EsmtpTranspor...
  • warninglog[17:51:53] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[17:51:53] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[17:51:53] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[17:51:53] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[17:51:53] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[17:51:53] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • Booting (11.31ms)
  • Application (660ms)
  • 1 x Application (98.25%)
    660.40ms
    1 x Booting (1.68%)
    11.31ms
    7 templates were rendered
    • themes.DevBlog.content.post (resources/views/themes/DevBlog/content/post.blade.php)34blade
      Params
      0
      post
      1
      postContent
      2
      author
      3
      updated_at
      4
      bing_rich_snippet_text
      5
      bing_rich_snippet_link
      6
      bing_related_keywords
      7
      google_related_keywords
      8
      bing_news_title
      9
      bing_news_description
      10
      bing_videos
      11
      bing_images
      12
      bing_search_result_title
      13
      bing_search_result_description
      14
      bing_search_result_url
      15
      bing_paa_questions
      16
      bing_paa_answers
      17
      bing_slider_faq_questions
      18
      bing_slider_faq_answers
      19
      bing_pop_faq_questions
      20
      bing_pop_faq_answers
      21
      bing_tab_faq_questions
      22
      bing_tab_faq_answers
      23
      google_faq_questions
      24
      google_faq_answers
      25
      google_rich_snippet
      26
      google_search_result
      27
      indexedArray
      28
      total_images
      29
      total_videos
      30
      settings
      31
      url_current
      32
      menus
      33
      sidebar
    • themes.DevBlog.layouts.master (resources/views/themes/DevBlog/layouts/master.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.head (resources/views/themes/DevBlog/panels/head.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.header (resources/views/themes/DevBlog/panels/header.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.navbar (resources/views/themes/DevBlog/panels/navbar.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.footer (resources/views/themes/DevBlog/panels/footer.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.scripts (resources/views/themes/DevBlog/panels/scripts.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    uri
    GET {post}
    middleware
    web, checkdate
    as
    post.show
    controller
    App\Http\Controllers\Frontend\json_data\PostController@show
    namespace
    where
    file
    app/Http/Controllers/Frontend/json_data/PostController.php:18-166
    7 statements were executed636ms
    • select * from `posts` where `published_at` <= '2025-06-11 17:51:53' and `slug` = 'what-is-the-relationship-between-a-stars-temperature-and-its-brightness' and `posts`.`deleted_at` is null limit 1
      2.31ms/app/Providers/RouteServiceProvider.php:54receivinghelpdeskask
      Metadata
      Bindings
      • 0. 2025-06-11 17:51:53
      • 1. what-is-the-relationship-between-a-stars-temperature-and-its-brightness
      Backtrace
      • 15. /app/Providers/RouteServiceProvider.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/Router.php:842
      • 19. Route binding:39
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/framework/src/Illuminate/Foundation/Http/Middleware/VerifyCsrfToken.php:78
    • select * from `json_post_contents` where `json_post_contents`.`post_id` = 204272 and `json_post_contents`.`post_id` is not null and `rewrite_id` = 0
      11.02msmiddleware::checkdate:30receivinghelpdeskask
      Metadata
      Bindings
      • 0. 204272
      • 1. 0
      Backtrace
      • 19. middleware::checkdate:30
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/jetstream/src/Http/Middleware/ShareInertiaData.php:61
      • 22. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:50
    • select * from `nova_menu_menus` where `slug` = 'header' limit 1
      610μs/vendor/outl1ne/nova-menu-builder/src/helpers.php:32receivinghelpdeskask
      Metadata
      Bindings
      • 0. header
      Backtrace
      • 15. /vendor/outl1ne/nova-menu-builder/src/helpers.php:32
      • 17. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
      • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`menu_id` = 1 and `nova_menu_menu_items`.`menu_id` is not null and `parent_id` is null order by `parent_id` asc, `order` asc, `name` asc
      340μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Bindings
      • 0. 1
      Backtrace
      • 19. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 20. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 22. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`parent_id` in (1) order by `order` asc
      310μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Backtrace
      • 24. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 25. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 27. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 28. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 29. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select `id`, `post_title`, `slug` from `posts` where `status` = 'publish' and `posts`.`deleted_at` is null order by RAND() limit 10
      620ms/app/View/Composers/SidebarView.php:22receivinghelpdeskask
      Metadata
      Bindings
      • 0. publish
      Backtrace
      • 14. /app/View/Composers/SidebarView.php:22
      • 15. /app/View/Composers/SidebarView.php:12
      • 16. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
      • 17. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
      • 20. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
    • select * from `fake_users` where `fake_users`.`id` = 13741 limit 1
      810μsview::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15receivinghelpdeskask
      Metadata
      Bindings
      • 0. 13741
      Backtrace
      • 21. view::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15
      • 23. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
      • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 25. /vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • 26. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
    App\Models\FakeUser
    1
    Outl1ne\MenuBuilder\Models\MenuItem
    1
    Outl1ne\MenuBuilder\Models\Menu
    1
    App\Models\JsonPostContent
    1
    App\Models\Post
    11
        _token
        kBl4cQ8IavgQIwp1FcvLb3asz50MkkSaV7QhrcPw
        _previous
        array:1 [ "url" => "https://receivinghelpdesk.com/ask/what-is-the-relationship-between-a-stars-tem...
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /what-is-the-relationship-between-a-stars-temperature-and-its-brightness
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:25 [ "cookie" => array:1 [ 0 => "_pk_id.64.7c30=1efce852eaff9293.1749644498.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6Im51dVFwU1FKbTdhTktkeTlIQS9mWVE9PSIsInZhbHVlIjoiOFZ0TXd4TGRlV2lZSTdrZjRVdTNUWEcySE02REdaSDI3MGRRMndDTFF1ZHlqQ0srZFk0RjZaK1NVYzlwMG8xRHh1dXFSR0FzMzdPN3R2YUpCSkwvb051U0ROckZ4NDZaaCtZaWZ2SlVsVVFVcFFVNnQyYnBBYmJBQjdLRWd1elUiLCJtYWMiOiI1MTkxZjM2YThkOTdmOTI5NDkzMTYwMjQzZGNlY2Q0YjRmZGU0M2RmMzI5Y2Y2YzFhNWI2NGEzOGEyMDVlNDA4IiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6IjBhRThLK1dJQlZVRjJPWUtBN0hXUkE9PSIsInZhbHVlIjoiWUNpL2F2SFJqVHFzalNzdG5BdUhORyt6M2lDOEpMQmxmTFdIZzZ6QXFTY1NMMkVwQWRwd1ZnMXZybDM3WGMxM2QyRVd2cEEyTEVkQm9hVCs2TEZxd2o0SFBPWGxhVlJ1RmRRN0JDSjIxanlJWDV5MUFqd2VnSjhKMER1aWR2cnEiLCJtYWMiOiI4ZGY2ZGRiOTcwMjYxNDEyZTc5YWQ5NWVmYzhjNjFjYWE4M2JjZmJhYjZlMWU2ZTk1YjI3YjJmZTIyZGM5MGI1IiwidGFnIjoiIn0%3D_pk_id.64.7c30=1efce852eaff9293.1749644498.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6Im51dVFwU1FKbTdhTktkeTlIQS9mWVE9PSIsInZhbHVlIjoiOFZ0TXd4TGRlV2lZSTdrZjRVdTNUW" ] "cf-ipcountry" => array:1 [ 0 => "US" ] "cf-connecting-ip" => array:1 [ 0 => "216.73.216.73" ] "cdn-loop" => array:1 [ 0 => "cloudflare; loops=1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "accept-encoding" => array:1 [ 0 => "gzip, br" ] "cf-ray" => array:1 [ 0 => "94e1121eac08cca4-ORD" ] "priority" => array:1 [ 0 => "u=0, i" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "cf-visitor" => array:1 [ 0 => "{"scheme":"https"}" ] "connection" => array:1 [ 0 => "close" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "216.73.216.73, 172.69.58.56" ] "x-server-addr" => array:1 [ 0 => "154.12.239.204" ] "host" => array:1 [ 0 => "receivinghelpdesk.com" ] ]
        request_server
        0 of 0
        array:56 [ "USER" => "runcloud" "HOME" => "/home/runcloud" "SCRIPT_NAME" => "/ask/index.php" "REQUEST_URI" => "/ask/what-is-the-relationship-between-a-stars-temperature-and-its-brightness" "QUERY_STRING" => "" "REQUEST_METHOD" => "GET" "SERVER_PROTOCOL" => "HTTP/1.0" "GATEWAY_INTERFACE" => "CGI/1.1" "REDIRECT_URL" => "/ask/what-is-the-relationship-between-a-stars-temperature-and-its-brightness" "REMOTE_PORT" => "55190" "SCRIPT_FILENAME" => "/home/runcloud/webapps/ReceivingHelpDesk/ask/index.php" "SERVER_ADMIN" => "you@example.com" "CONTEXT_DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "CONTEXT_PREFIX" => "" "REQUEST_SCHEME" => "http" "DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "REMOTE_ADDR" => "172.69.58.56" "SERVER_PORT" => "80" "SERVER_ADDR" => "127.0.0.1" "SERVER_NAME" => "receivinghelpdesk.com" "SERVER_SOFTWARE" => "Apache/2.4.63 (Unix) OpenSSL/1.1.1f" "SERVER_SIGNATURE" => "" "LD_LIBRARY_PATH" => "/RunCloud/Packages/apache2-rc/lib" "PATH" => "/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin" "HTTP_COOKIE" => "_pk_id.64.7c30=1efce852eaff9293.1749644498.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6Im51dVFwU1FKbTdhTktkeTlIQS9mWVE9PSIsInZhbHVlIjoiOFZ0TXd4TGRlV2lZSTdrZjRVdTNUWEcySE02REdaSDI3MGRRMndDTFF1ZHlqQ0srZFk0RjZaK1NVYzlwMG8xRHh1dXFSR0FzMzdPN3R2YUpCSkwvb051U0ROckZ4NDZaaCtZaWZ2SlVsVVFVcFFVNnQyYnBBYmJBQjdLRWd1elUiLCJtYWMiOiI1MTkxZjM2YThkOTdmOTI5NDkzMTYwMjQzZGNlY2Q0YjRmZGU0M2RmMzI5Y2Y2YzFhNWI2NGEzOGEyMDVlNDA4IiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6IjBhRThLK1dJQlZVRjJPWUtBN0hXUkE9PSIsInZhbHVlIjoiWUNpL2F2SFJqVHFzalNzdG5BdUhORyt6M2lDOEpMQmxmTFdIZzZ6QXFTY1NMMkVwQWRwd1ZnMXZybDM3WGMxM2QyRVd2cEEyTEVkQm9hVCs2TEZxd2o0SFBPWGxhVlJ1RmRRN0JDSjIxanlJWDV5MUFqd2VnSjhKMER1aWR2cnEiLCJtYWMiOiI4ZGY2ZGRiOTcwMjYxNDEyZTc5YWQ5NWVmYzhjNjFjYWE4M2JjZmJhYjZlMWU2ZTk1YjI3YjJmZTIyZGM5MGI1IiwidGFnIjoiIn0%3D_pk_id.64.7c30=1efce852eaff9293.1749644498.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6Im51dVFwU1FKbTdhTktkeTlIQS9mWVE9PSIsInZhbHVlIjoiOFZ0TXd4TGRlV2lZSTdrZjRVdTNUW" "HTTP_CF_IPCOUNTRY" => "US" "HTTP_CF_CONNECTING_IP" => "216.73.216.73" "HTTP_CDN_LOOP" => "cloudflare; loops=1" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_ACCEPT_ENCODING" => "gzip, br" "HTTP_CF_RAY" => "94e1121eac08cca4-ORD" "HTTP_PRIORITY" => "u=0, i" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_CF_VISITOR" => "{"scheme":"https"}" "HTTP_CONNECTION" => "close" "HTTP_X_FORWARDED_PROTO" => "https" "HTTP_X_FORWARDED_FOR" => "216.73.216.73, 172.69.58.56" "HTTP_X_SERVER_ADDR" => "154.12.239.204" "HTTP_HOST" => "receivinghelpdesk.com" "HTTPS" => "on" "REDIRECT_STATUS" => "200" "REDIRECT_HTTPS" => "on" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/ask/index.php" "REQUEST_TIME_FLOAT" => 1749644513.0815 "REQUEST_TIME" => 1749644513 ]
        request_cookies
        0 of 0
        array:4 [ "_pk_id_64_7c30" => null "_pk_ses_64_7c30" => null "XSRF-TOKEN" => "kBl4cQ8IavgQIwp1FcvLb3asz50MkkSaV7QhrcPw" "askhelpdesk_session" => "SrYsnVhydQglW8sh6PsHbAR1VWZAby1bhcv1hje6" ]
        response_headers
        0 of 0
        array:7 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "private, must-revalidate" ] "date" => array:1 [ 0 => "Wed, 11 Jun 2025 12:21:53 GMT" ] "pragma" => array:1 [ 0 => "no-cache" ] "expires" => array:1 [ 0 => -1 ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6InoyS0hKU1d0aDk3VXkzUjg2ZkZ1Nmc9PSIsInZhbHVlIjoicFhsSnQrSEFtUlpHMEZGYzljbW1vL1psNXNMMXNZQVhrOTJROG5BZ3BCdXMreDdBbGdiTWRNK1pLck1kY2FkRW1Fb2Y1RjkwUE1Cc1JKWUFKd0lxSWt5ZDc3czBybW0yMnZCOUU2UXFIbTM3eHJiVzBIWGpWMjhuamUrSzI4TkUiLCJtYWMiOiI2MDMzNWI0YWRkOGQwNDJlMGRjODRjMjAxYzA4ZDZlYmNlMDQ5OWMzNThlNjViNmMwNWNmY2UzOThmODc1MzlmIiwidGFnIjoiIn0%3D; expires=Wed, 11-Jun-2025 14:21:53 GMT; Max-Age=7200; path=/; samesite=laxXSRF-TOKEN=eyJpdiI6InoyS0hKU1d0aDk3VXkzUjg2ZkZ1Nmc9PSIsInZhbHVlIjoicFhsSnQrSEFtUlpHMEZGYzljbW1vL1psNXNMMXNZQVhrOTJROG5BZ3BCdXMreDdBbGdiTWRNK1pLck1kY2FkRW1Fb2Y1R" 1 => "askhelpdesk_session=eyJpdiI6IjdFSTd1dWMwWHNldDNtOUVXMkgvTUE9PSIsInZhbHVlIjoiKzFGejRqMHFvNDl1TEpWbllRa0RVV0Y5YytQbGpYdkwrQ2tTWVp4RncvcHA3dTBmTEw5Y0dGUzVPYVV2bVFYazd3Sld2MWs0TWNSMXNkYkp3MXh3UWJvc1Vsd2pKajRBVVpuVkVGUnBWQzl2c2taTnJQY0hpVkwzeWVjcHdVY1IiLCJtYWMiOiJlYTYzODdjNWZlMjcyZGNlMzNkYzgzMmJkNWI1YzBhZDNmOTMyYjEyNWEyNWMzZjdjZjFmODM3NWJlNTNjMjYzIiwidGFnIjoiIn0%3D; expires=Wed, 11-Jun-2025 14:21:53 GMT; Max-Age=7200; path=/; httponly; samesite=laxaskhelpdesk_session=eyJpdiI6IjdFSTd1dWMwWHNldDNtOUVXMkgvTUE9PSIsInZhbHVlIjoiKzFGejRqMHFvNDl1TEpWbllRa0RVV0Y5YytQbGpYdkwrQ2tTWVp4RncvcHA3dTBmTEw5Y0dGUzVPYVV2bVFY" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6InoyS0hKU1d0aDk3VXkzUjg2ZkZ1Nmc9PSIsInZhbHVlIjoicFhsSnQrSEFtUlpHMEZGYzljbW1vL1psNXNMMXNZQVhrOTJROG5BZ3BCdXMreDdBbGdiTWRNK1pLck1kY2FkRW1Fb2Y1RjkwUE1Cc1JKWUFKd0lxSWt5ZDc3czBybW0yMnZCOUU2UXFIbTM3eHJiVzBIWGpWMjhuamUrSzI4TkUiLCJtYWMiOiI2MDMzNWI0YWRkOGQwNDJlMGRjODRjMjAxYzA4ZDZlYmNlMDQ5OWMzNThlNjViNmMwNWNmY2UzOThmODc1MzlmIiwidGFnIjoiIn0%3D; expires=Wed, 11-Jun-2025 14:21:53 GMT; path=/XSRF-TOKEN=eyJpdiI6InoyS0hKU1d0aDk3VXkzUjg2ZkZ1Nmc9PSIsInZhbHVlIjoicFhsSnQrSEFtUlpHMEZGYzljbW1vL1psNXNMMXNZQVhrOTJROG5BZ3BCdXMreDdBbGdiTWRNK1pLck1kY2FkRW1Fb2Y1R" 1 => "askhelpdesk_session=eyJpdiI6IjdFSTd1dWMwWHNldDNtOUVXMkgvTUE9PSIsInZhbHVlIjoiKzFGejRqMHFvNDl1TEpWbllRa0RVV0Y5YytQbGpYdkwrQ2tTWVp4RncvcHA3dTBmTEw5Y0dGUzVPYVV2bVFYazd3Sld2MWs0TWNSMXNkYkp3MXh3UWJvc1Vsd2pKajRBVVpuVkVGUnBWQzl2c2taTnJQY0hpVkwzeWVjcHdVY1IiLCJtYWMiOiJlYTYzODdjNWZlMjcyZGNlMzNkYzgzMmJkNWI1YzBhZDNmOTMyYjEyNWEyNWMzZjdjZjFmODM3NWJlNTNjMjYzIiwidGFnIjoiIn0%3D; expires=Wed, 11-Jun-2025 14:21:53 GMT; path=/; httponlyaskhelpdesk_session=eyJpdiI6IjdFSTd1dWMwWHNldDNtOUVXMkgvTUE9PSIsInZhbHVlIjoiKzFGejRqMHFvNDl1TEpWbllRa0RVV0Y5YytQbGpYdkwrQ2tTWVp4RncvcHA3dTBmTEw5Y0dGUzVPYVV2bVFY" ] ]
        session_attributes
        0 of 0
        array:4 [ "_token" => "kBl4cQ8IavgQIwp1FcvLb3asz50MkkSaV7QhrcPw" "_previous" => array:1 [ "url" => "https://receivinghelpdesk.com/ask/what-is-the-relationship-between-a-stars-temperature-and-its-brightness" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]